# Probing Cosmic Inflation with the LiteBIRD Cosmic Microwave Background Polarization Survey

E. Allys, K. Arnold, J. Aumont, R. Aurlien, S. Azzoni, C. Baccigalupi, A.J.

Banday, R. Banerji, R.B. Barreiro, N. Bartolo, et al.

► To cite this version:

E. Allys, K. Arnold, J. Aumont, R. Aurlien, S. Azzoni, et al. Probing Cosmic Inflation with the LiteBIRD Cosmic Microwave Background Polarization Survey. PTEP, 2023, 2023 (4), pp.042F01. 10.1093/ptep/ptac150. hal-03588988

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Submitted on 10 Nov 2023

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# Probing cosmic inflation with the *LiteBIRD* cosmic microwave background polarization survey

LiteBIRD Collaboration, E. Allys<fnref n="1" />, K. Arnold², J. Aumont³, R. Aurlien⁴,
S. Azzoni⁵,⁶, C. Baccigalupi⁷,⁸,⁹, A. J. Banday³, R. Banerji⁴, R. B. Barreiro¹⁰,
N. Bartolo¹¹,¹²,¹³, L. Bautista³, D. Beck¹⁴, S. Beckman¹⁵, M. Bersanelli¹⁶,¹⁷,
F. Boulanger<fnref n="1" />, M. Brilenkov⁴, M. Bucher¹⁸, E. Calabrese¹⁹, P. Campeti²⁰,
A. Carones²¹,²², F. J. Casas¹⁰, A. Catalano²³, V. Chan²⁴, K. Cheung¹⁵,²⁵,²⁶,
Y. Chinone⁶,²⁷, S. E. Clark¹⁴,²⁸, F. Columbro²⁹,³⁰, G. D'Alessandro²⁹,³⁰,
P. de Bernardis²⁹,³⁰, T. de Haan³¹, E. de la Hoz¹⁰,³², M. De Petris²⁹,³⁰, S. Della Torre³³,
P. Diego-Palazuelos¹⁰,³², M. Dobbs³⁴, T. Dotani³⁵,³⁶, J. M. Duval³⁷, T. Elleflot³⁸,
H. K. Eriksen⁴, J. Errard¹⁸, T. Essinger-Hileman³⁹, F. Finelli⁴⁰,⁴¹, R. Flauger²,
C. Franceschet¹⁶,¹⁷, U. Fuskeland⁴, M. Galloway⁴, K. Ganga¹⁸, M. Gerbino⁴²,
M. Gervasi³³,⁴³, R. T. Génova-Santos⁴⁴,⁴⁵, T. Ghigna⁵,⁶, S. Giardiello⁴⁶, E. Gjerløw⁴,
J. Grain⁴⁷, F. Grupp⁴⁸, A. Gruppuso⁴⁰,⁴¹, J. E. Gudmundsson⁴⁹, N. W. Halverson⁵⁰,
P. Hargrave¹⁹, T. Hasebe⁶, M. Hasegawa³¹,³⁶,⁵¹, M. Hazumi⁶,³¹,³⁵,³⁶,⁵¹,
S. Henrot-Versillé⁵², B. Hensley⁵³, L. T. Hergt⁵⁴, D. Herman⁴, E. Hivon⁵⁵,
R. A. Hlozek²⁴, A. L. Hornsby¹⁵, Y. Hoshino⁵⁶, J. Hubmayr⁵⁷, K. Ichiki⁵⁸, T. Iida⁵⁹,
H. Imada⁶⁰, H. Ishino⁶¹, G. Jaehnig⁵⁰, N. Katayama⁶, A. Kato³¹, R. Keskitalo¹⁵,²⁵,²⁶,
T. Kisner²⁶, Y. Kobayashi⁶², A. Kogut³⁹, K. Kohri³¹, E. Komatsu⁶,²⁰, K. Komatsu⁶¹,
K. Konishi⁶³, N. Krachmalnicoff⁷,⁸,⁹, C. L. Kuo¹⁴,⁶⁴, L. Lamagna²⁹,³⁰, M. Lattanzi⁴²,
A. T. Lee¹⁵,³⁸,⁵¹, C. Leloup¹⁸, F. Levrier<fnref n="1" />, E. Linder²⁵,³⁸, G. Luzzi⁶⁵, J. Macias-Perez²³,
T. Maciaszek⁶⁶, B. Maffei⁴⁷, D. Maino¹⁶, S. Mandelli¹⁶,¹⁷, E. Martínez-González¹⁰,
S. Masi²⁹,³⁰, M. Massa⁶⁷, S. Matarrese¹¹,¹²,¹³,⁶⁸, F. T. Matsuda³⁵, T. Matsumura⁶,
L. Mele²⁹,³⁰, M. Migliaccio²¹,²², Y. Minami⁶⁹, A. Moggi⁶⁷, J. Montgomery³⁴,
L. Montier³, G. Morgante⁴⁰, B. Mot³, Y. Nagano⁶¹, T. Nagasaki³¹, R. Nagata³⁵,
R. Nakano³⁵,⁷⁰, T. Namikawa⁶, F. Nati³³,⁴³, P. Natoli⁴²,⁴⁶, S. Nerval²⁴, F. Noviello¹⁹,
K. Odagiri³⁵, S. Oguri³⁵, H. Ohsaki⁶², L. Pagano⁴²,⁴⁶,⁴⁷, A. Paiella²⁹,³⁰, D. Paoletti⁴⁰,⁴¹,
A. Passerini³³,⁴³, G. Patanchon¹⁸, F. Piacentini²⁹,³⁰, M. Piat¹⁸, G. Pisano¹⁹,²⁹,³⁰,
G. Polenta⁶⁵, D. Poletti³³,⁴³, T. Prouvé³⁷, G. Puglisi²¹,²⁶, D. Rambaud³, C. Raum¹⁵,
S. Realini¹⁶, M. Reinecke²⁰, M. Remazeilles¹⁰,⁷¹, A. Ritacco<fnref n="1" />,⁴⁷,⁷², G. Roudil³,
J. A. Rubino-Martin⁴⁴,⁴⁵, M. Russell², H. Sakurai⁶², Y. Sakurai⁶,⁶¹, M. Sasaki⁷³,
D. Scott⁵⁴, Y. Sekimoto³¹,³⁵,⁷⁰, K. Shinozaki⁷⁴, M. Shiraishi⁷⁵, P. Shirron³⁹,
G. Signorelli⁶⁷, F. Spinella⁶⁷, S. Stever⁶,⁶¹, R. Stompor¹⁸,⁷⁶, S. Sugiyama⁵⁶,
R. M. Sullivan⁵⁴, A. Suzuki²⁶, T. L. Svalheim⁴, E. Switzer³⁹, R. Takaku³⁵,⁷⁷,
H. Takakura³⁵,⁷⁰, Y. Takase⁶¹, A. Tartari⁶⁷,⁷⁸, Y. Terao⁶², J. Thermeau¹⁸,
H. Thommesen⁴, K. L. Thompson¹⁴,⁶⁴, M. Tomasi¹⁶,¹⁷, M. Tominaga³⁵,⁷⁰,
M. Tristram⁵², M. Tsuji⁷⁹, M. Tsujimoto³⁵, L. Vacher³, P. Vielva¹⁰, N. Vittorio²¹,²²,
W. Wang¹⁸, K. Watanuki³⁵, I. K. Wehus⁴, J. Weller⁴⁸, B. Westbrook¹⁵, J. Wilms⁷³,
B. Winter⁸⁰,⁸¹, E. J. Wollack³⁹, J. Yumoto⁶², and M. Zannoni³³,⁴³

<footnote n="1">¹Laboratoire de Physique de l'École Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, F-75005 Paris, France</footnote>
<footnote n="2">²University of California, San Diego, Department of Physics, San Diego, CA 92093-0424, USA</footnote>

<footnote n="3">³IRAP, Université de Toulouse, (Toulouse), 9, avenue du Colonel Roche BP 44346 31028 Toulouse Cedex 4, France</footnote>

<footnote n="4">⁴Institute of Theoretical Astrophysics, University of Oslo, Blindern 0315, OSLO, Norway</footnote>

<footnote n="5">⁵Department of Physics, University of Oxford, Denys Wilkinson Building, Keble Road, Oxford OX1 3RH, UK</footnote>

<footnote n="6">⁶Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU, WPI), UTIAS, The University of Tokyo, Kashiwa, Chiba 277-8583, Japan</footnote>

<footnote n="7">⁷International School for Advanced Studies (SISSA), Via Bonomea 265, I-34136 Trieste, Italy</footnote>

<footnote n="8">⁸INFN Sezione di Trieste, Via Valerio 2, I-34127 Trieste, Italy</footnote>

<footnote n="9">⁹IFPU, Via Beirut, 2, I-34151 Grignano, Trieste, Italy</footnote>

<footnote n="10">¹⁰Instituto de Fisica de Cantabria (IFCA, CSIC-UC), Avenida los Castros SN, E-39005 Santander, Spain</footnote>

<footnote n="11">¹¹Dipartimento di Fisica e Astronomia “G. Galilei”, Università degli Studi di Padova, Via Marzolo 8, I-35131 Padova, Italy</footnote>

<footnote n="12">¹²INFN Sezione di Padova, Via Marzolo 8, I-35131 Padova, Italy</footnote>

<footnote n="13">¹³INAF, Osservatorio Astronomico di Padova, Vicolo dell'Osservatorio 5, I-35122 Padova, Italy</footnote>

<footnote n="14">¹⁴Stanford University, Department of Physics, CA 94305-4060, USA</footnote>

<footnote n="15">¹⁵University of California, Berkeley, Department of Physics, Berkeley, CA 94720, USA</footnote>

<footnote n="16">¹⁶Dipartimento di Fisica, Università degli Studi di Milano, Via Celoria 16, I-20133 Milano, Italy</footnote>

<footnote n="17">¹⁷INFN Sezione di Milano, Via Celoria 16, I-20133 Milano, Italy</footnote>

<footnote n="18">¹⁸Université de Paris, CNRS, Astroparticule et Cosmologie, F-75013 Paris, France</footnote>

<footnote n="19">¹⁹School of Physics and Astronomy, Cardiff University, Cardiff CF24 3AA, UK</footnote>

<footnote n="20">²⁰Max Planck Institute for Astrophysics, Karl-Schwarzschild-Str. 1, D-85748 Garching, Germany</footnote>

<footnote n="21">²¹Dipartimento di Fisica, Università di Roma Tor Vergata, Via della Ricerca Scientifica 1, I-00133 Roma, Italy</footnote>

<footnote n="22">²²INFN Sezione di Roma2, Università di Roma Tor Vergata, Via della Ricerca Scientifica 1, I-00133 Roma, Italy</footnote>

<footnote n="23">²³Univ. Grenoble Alpes, CNRS, LPSC-IN2P3, 53 avenue des Martyrs, F-38000 Grenoble, France</footnote>

<footnote n="24">²⁴David A. Dunlap Department of Astronomy and Astrophysics, 50 St George Street, Toronto, ON M5S 3H4, Canada</footnote>

<footnote n="25">²⁵University of California, Berkeley, Space Sciences Laboratory, Berkeley, CA 94720, USA</footnote>

<footnote n="26">²⁶Lawrence Berkeley National Laboratory (LBNL), Computational Cosmology Center, Berkeley, CA 94720, USA</footnote>

<footnote n="27">²⁷University of Tokyo, School of Science, Research Center for the Early Universe, RESCEU, Tokyo 113-0033, Japan</footnote>

<footnote n="28">²⁸Kavli Institute for Particle Astrophysics and Cosmology (KIPAC), Stanford University, Stanford, CA 94305, USA</footnote>

<footnote n="29">²⁹Dipartimento di Fisica, Università La Sapienza, P.le A. Moro 2, I-00185 Roma, Italy</footnote>

<footnote n="30">³⁰INFN Sezione di Roma, P.le A. Moro 2, I-00185 Roma, Italy</footnote>

<footnote n="31">³¹Institute of Particle and Nuclear Studies (IPNS), High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305-0801, Japan</footnote>

<footnote n="32">³²Dpto. de Fisica Moderna, Universidad de Cantabria, Avda. los Castros s/n, E-39005 Santander, Spain</footnote>

<footnote n="33">³³INFN Sezione Milano Bicocca, Piazza della Scienza 3, I-20126 Milano, Italy</footnote>

<footnote n="34">³⁴McGill University, Physics Department, Montreal, QC H3A 0G4, Canada</footnote>

<footnote n="35">³⁵Japan Aerospace Exploration Agency (JAXA), Institute of Space and Astronautical Science (ISAS), Sagamihara, Kanagawa 252-5210, Japan</footnote>

<footnote n="36">³⁶The Graduate University for Advanced Studies (SOKENDAI), Miura District, Kanagawa 240-0115, Hayama, Japan</footnote>

<footnote n="37">³⁷Université Grenoble Alpes, CEA, IRIG-DSBT, F-38000 Grenoble, France</footnote>

<footnote n="38">³⁸Lawrence Berkeley National Laboratory (LBNL), Physics Division, Berkeley, CA 94720, USA</footnote>

<footnote n="39">³⁹NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA</footnote>

<footnote n="40">⁴⁰INAF - OAS Bologna, Via Piero Gobetti 93/3, I-40129 Bologna, Italy</footnote>

<footnote n="41">⁴¹INFN Sezione di Bologna, Viale C. Berti Pichat 6/2, I-40127 Bologna, Italy</footnote>

<footnote n="42">⁴²INFN Sezione di Ferrara, Via Saragat 1, I-44122 Ferrara, Italy</footnote>

<footnote n="43">⁴³University of Milano Bicocca, Physics Department, P.zza della Scienza 3, I-20126 Milan, Italy</footnote>
⁴⁴Instituto de Astrofísica de Canarias, E-38200 La Laguna, Tenerife, Canary Islands, Spain

⁴⁵Departamento de Astrofísica, Universidad de La Laguna (ULL), E-38206 La Laguna, Tenerife, Spain

⁴⁶Dipartimento di Fisica e Scienze della Terra, Università di Ferrara, Via Saragat 1, I-44122 Ferrara, Italy

⁴⁷Université Paris-Saclay, CNRS, Institut d'Astrophysique Spatiale, F-91405 Orsay, France

⁴⁸Universitäts-Sternwarte, Fakultät für Physik, Ludwig-Maximilians Universität München, Scheinerstr. 1, D-81679 München, Germany

⁴⁹The Oskar Klein Centre, Department of Physics, Stockholm University, SE-106 91 Stockholm, Sweden

⁵⁰Center for Astrophysics and Space Astronomy, University of Colorado, Boulder, CO 80309, USA

⁵¹International Center for Quantum-field Measurement Systems for Studies of the Universe and Particles (QUP), High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305-0801, Japan

⁵²Université Paris-Saclay, CNRS/IN2P3, IJCLab, F-91405 Orsay, France

⁵³Department of Astrophysical Sciences, Peyton Hall, Princeton University, Princeton, NJ 08544, USA

⁵⁴Department of Physics and Astronomy, University of British Columbia, 6224 Agricultural Road, Vancouver, BC V6T 1Z1, Canada

⁵⁵Institut d'Astrophysique de Paris, CNRS/Sorbonne Université, 75014 Paris, France

⁵⁶Saitama University, Saitama 338-8570, Japan

⁵⁷NIST Quantum Sensors Group, 325 Broadway, Boulder, CO 80305, USA

⁵⁸Nagoya University, Kobayashi-Masukawa Institute for the Origin of Particle and the Universe, Aichi 464-8602, Japan

⁵⁹ispace, inc., Tokyo 103-0007, Japan

⁶⁰National Astronomical Observatory of Japan, Mitaka, Tokyo 181-8588, Japan

⁶¹Okayama University, Department of Physics, Okayama 700-8530, Japan

⁶²The Institute for Solid State Physics (ISSP), The University of Tokyo, Kashiwa, Chiba 277-8581, Japan

⁶³The University of Tokyo, Institute for Photon Science and Technology, Tokyo 113-0033, Japan

⁶⁴SLAC National Accelerator Laboratory, Kavli Institute for Particle Astrophysics and Cosmology (KIPAC), Menlo Park, CA 94025, USA

⁶⁵Space Science Data Center, Italian Space Agency, Via del Politecnico, I-00133 Roma, Italy

⁶⁶Centre National d'Etudes Spatiales (CNES), 18 avenue Edouard Belin 31 401 TOULOUSE CEDEX 4, France

⁶⁷INFN Sezione di Pisa, Largo Bruno Pontecorvo 3, I-56127 Pisa, Italy

⁶⁸Gran Sasso Science Institute (GSSI), Viale F. Crispi 7, I-67100, L'Aquila, Italy

⁶⁹Research Center for Nuclear Physics, Osaka University, Ibaraki, Osaka 567-0047, Japan

⁷⁰The University of Tokyo, Department of Astronomy, Tokyo 113-0033, Japan

⁷¹Jodrell Bank Centre for Astrophysics, Department of Physics and Astronomy, School of Natural Sciences, The University of Manchester, Oxford Road, Manchester M13 9PL, UK

⁷²INAF-Osservatorio Astronomico di Cagliari, Via della Scienza 5, I-09047 Selargius, Italy

⁷³Remeis-Observatory and Erlangen Centre for Astroparticle Physics, FAU Erlangen-Nürnberg, Sternwartstr. 7, D-96049 Bamberg, Germany

⁷⁴Japan Aerospace Exploration Agency (JAXA), Research and Development Directorate, Tsukuba, Ibaraki 305-8505, Japan

⁷⁵School of General and Management Studies, Suwa University of Science, 5000-1 Toyohira, Chino, Nagano 391-0292, Japan

⁷⁶CNRS-UCB International Research Laboratory, Centre Pierre Binétruy, UMI2007, Berkeley, CA 94720, USA

⁷⁷The University of Tokyo, Department of Physics, Tokyo 113-0033, Japan

⁷⁸Dipartimento di Fisica, Università di Pisa, Largo B. Pontecorvo 3, I-56127 Pisa, Italy

⁷⁹National Institute of Technology, Kagawa College, Kagawa 761-8058, Japan

⁸⁰Physics and Astronomy Dept., University College London (UCL), London

⁸¹Mullard Space Science Laboratory, University College London, London

*E-mail: litebird_authors@ml.post.kek.jp

Received February 8, 2022; Revised October 31, 2022; Accepted November 4, 2022; Published November 21, 2022
LiteBIRD, the Lite (Light) satellite for the study of B-mode polarization and Inflation from cosmic background Radiation Detection, is a space mission for primordial cosmology and fundamental physics. The Japan Aerospace Exploration Agency (JAXA) selected LiteBIRD in May 2019 as a strategic large-class (L-class) mission, with an expected launch in the late 2020s using JAXA's H3 rocket. LiteBIRD is planned to orbit the Sun-Earth Lagrangian point L2, where it will map the cosmic microwave background polarization over the entire sky for three years, with three telescopes in 15 frequency bands between 34 and 448 GHz, to achieve an unprecedented total sensitivity of 2.2 µK-arcmin, with a typical angular resolution of 0.5° at 100 GHz. The primary scientific objective of LiteBIRD is to search for the signal from cosmic inflation, either making a discovery or ruling out well-motivated inflationary models. The measurements of LiteBIRD will also provide us with insight into the quantum nature of gravity and other new physics beyond the standard models of particle physics and cosmology. We provide an overview of the LiteBIRD project, including scientific objectives, mission and system requirements, operation concept, spacecraft and payload module design, expected scientific outcomes, potential design extensions, and synergies with other projects.

Subject Index F14

# 1. Introduction

## 1.1. CMB polarization as the new frontier and the LiteBIRD satellite

Observations of cosmic microwave background (CMB) temperature fluctuations have played a pivotal role in establishing the standard cosmological model, called the Λ cold dark matter model [1], and provide insights into the origin of structure, the density of baryons, dark matter, dark energy, the number of neutrino species, and the global properties of spacetime [2–5]. Observations have reached a point at which most of the information about the early Universe available in temperature fluctuations has been exhausted [6,7]. However, precise measurements of the fainter CMB polarization anisotropies hold the key to answering many remaining questions about the Universe. Observations have so far only begun to scratch the surface [8–13].

Perhaps the biggest remaining question is what mechanism created the small primordial fluctuations that seeded the observed CMB anisotropies and eventually grew into stars and galaxies. The most widely studied idea is “cosmic inflation” [14–19]. According to this idea, the primordial fluctuations originated as quantum fluctuations during a period of nearly exponential expansion of the very early Universe [20–24]. Eventually this period ended and the Universe became filled with a hot and dense plasma that subsequently cooled and led to the Universe that we see around us. As a consequence of the nearly exponential expansion that stretched microscopic regions of spacetimes to macroscopic scales, the plasma is homogeneous and isotropic, except for the minute quantum fluctuations that were also stretched to macroscopic scales.

Cosmic inflation predicts primordial density fluctuations that are consistent with the observed temperature fluctuations [20–24]. In addition, inflation predicts quantum fluctuations in the fabric of spacetime itself [25,26]. These primordial gravitational waves lead to a characteristic imprint in CMB polarization, commonly referred to as “B-mode” polarization [27–29], and many of the best-motivated models predict a signal that is large enough to be detected with LiteBIRD (the Lite (Light) satellite for the study of B-mode polarization and Inflation from cosmic background Radiation Detection) [30].

A detection of this signal would open an unexplored frontier of physics, shedding light on fundamental processes at energies far beyond the reach of CERN's Large Hadron Collider,
revolutionizing our understanding of physics and the early Universe [31]. A detection of primordial gravitational waves with *LiteBIRD* would have important implications for many aspects of fundamental physics. A detection would, for instance, indicate that inflation occurred near the energy scale associated with grand unified theories, providing additional evidence in favor of the idea of the unification of forces. Knowledge of the energy scale of inflation also has important implications for several other aspects of fundamental physics, such as axions and, in the context of string theory, the fields that control the shapes and sizes of the compact dimensions.

To search for the imprint of gravitational waves, *LiteBIRD* will conduct a survey of the entire sky that is 30 times more sensitive than previous full-sky experiments, corresponding to a raw sensitivity of nearly 1000 *Planck* missions.<fnref n="1" /> *LiteBIRD* will be the natural next step in the series of CMB space missions, following National Aeronautics and Space Administration (NASA)'s *COBE* [32] and *WMAP* [33], and the European Space Agency (ESA)'s *Planck* [34], each of which has made its own landmark scientific discoveries. See Ref. [2] for a comprehensive list of CMB experiments and their pioneering contributions.

The CMB polarization anisotropies can be decomposed according to their transformation properties under parity transformations into “*E*-modes” and “*B*-modes”. The *E*-mode polarization is predominantly caused by acoustic waves present at recombination, and the signal is strongest on angular scales of a few to tens of arcminutes (corresponding to multipoles of $\ell \sim 1000$). The *B*-mode polarization pattern imprinted by gravitational waves peaks on degree angular scales (corresponding to multipoles of $\ell \simeq 80$) and on very large angular scales (corresponding to multipoles of $\ell \lesssim 10$) [27,35]. The “recombination peak” near $\ell \simeq 80$ is imprinted during the epoch when electrons and protons combine to form hydrogen and the Universe becomes neutral, while the “reionization bump” below $\ell \simeq 10$ is imprinted around the time when the first stars reionize the Universe [36]. At linear order, the density perturbations do not generate *B*-mode polarization, which makes the *B*-mode power spectrum the most natural observable to search for primordial gravitational waves. However, CMB photons are deflected by the gravitational potentials associated with the matter along the line of sight. This is referred to as weak gravitational lensing and converts some of the “*E*-mode” polarization generated by density perturbations into *B*-modes [37]. Like the *E*-modes, this effect peaks on much smaller scales of a few arcminutes (corresponding to multipoles of $\ell \simeq 1000$) but must be taken into account. This contribution is well understood theoretically, and *LiteBIRD* targets any excess over the lensing signal caused by the imprint of gravitational waves. While ground-based experiments only target the recombination peak, *LiteBIRD* can see both peaks in the *B*-mode power spectrum.

In addition to the *B*-modes caused by weak gravitational lensing of *E*-modes, there are additional “foreground” sources of *B*-mode polarization at microwave frequencies. Thermal emission by interstellar dust grains that are aligned with the Galactic magnetic field and synchrotron emission from electrons spiraling in the Galactic magnetic field provide the dominant contributions. Fortunately, the frequency dependence of the primordial signal and foreground emission differ significantly so that multi-frequency observations allow us to disentangle the primordial and foreground contributions [38–40].

<footnote n="1">¹This is based on a comparison between the inverse-variance weighted combination of the white noise for CMB polarization of all channels for *LiteBIRD* versus *Planck*.</footnote>
<figure><img src="image_2.png" /><figcaption>**Fig. 1.** CMB power spectra of the temperature anisotropy (top), *E*-mode polarization (middle), and *B*-mode polarization (bottom). The solid lines show the angular power spectra for the best-fitting ΛCDM model in the presence of a scale-invariant tensor (gravitational wave) perturbation with a tensor-to-scalar ratio parameter of *r* = 0.004. The thin dashed line shows the contribution to the *B*-mode spectrum from scale-invariant tensor perturbation with *r* = 0.004. A summary of present measurements of CMB power spectra (colored points) [8–10,12,41–47] and the expected polarization sensitivity of *LiteBIRD* (black points) are also shown.</figcaption></figure>

To separate these primordial and foreground components, *LiteBIRD* will survey the full sky in 15 frequency bands from 34 to 448 GHz, with effective polarization sensitivity of 2 μK-arcmin and angular resolution of 31 arcmin (at 140 GHz). Rapid polarization modulation, a densely linked observation strategy, and the stable environment of an orbit around L2 (the second Lagrangian point for the Sun–Earth system) provide unprecedented ability to control systematic errors, especially on the largest angular scales below $\ell \simeq 10$. Taken together, the control of foregrounds and systematic errors gives *LiteBIRD* the ability to detect both the reionization and recombination bumps in the *B*-mode power spectrum, giving much higher confidence that a primordial signal has been uncovered. Importantly, if a hint of the recombination peak is seen by a ground-based or balloon-borne experiment, *LiteBIRD* will make a definitive statement on the detection of the signal and greatly improve the quantitative constraints on the physics of inflation. The forecast for *LiteBIRD*'s ability to measure the primordial *B*-mode power spectrum is shown in Fig. 1, together with currently available measurements.
Even in the absence of gravitational waves, on the largest angular scales, scattering of photons during the reionization epoch at $z \simeq 6-10$ generates *E*-mode polarization [36]. *LiteBIRD* will measure this signal with high precision and will make a definitive determination of the optical depth to the surface of last scattering. The optical depth contains key information about the nature of the epoch of reionization and will, for instance, constrain models of the first stars. The optical depth is currently the least well-constrained parameter of the standard cosmological model and currently limits any constraints that rely on comparisons of the amplitude of CMB anisotropies and clustering of the matter distribution, such as the measurement of the sum of neutrino masses [48–52]. *LiteBIRD* will provide a cosmic-variance-limited measurement<fnref n="2" /> of *E*-modes at low multipoles. This will complement measurements by high-resolution ground-based CMB experiments such as the South Pole Observatory (SPO) [57], Simons Observatory (SO) [58], and CMB Stage-4 [59] and will significantly improve cosmological measurements of the sum of neutrino masses.

Finally, the *LiteBIRD* all-sky polarized maps in 15 frequency bands will be a rich legacy data set for understanding the large-scale magnetic field structure in the Milky Way, having five times greater sensitivity to Galactic magnetic fields than ESA’s *Planck* mission [60,61].

## 1.2. *Outline of this review*

This paper is arranged as follows. Section 2 introduces CMB *B*-mode tests of cosmic inflation, including constraints expected by *LiteBIRD* and an argument for the necessity of CMB *B*-mode measurements from space. Section 3 gives a broad overview of the *LiteBIRD* mission, including the science requirements, a description of the instrument, and a description of flight operations. Section 4 describes the *LiteBIRD* instrument, including the telescope designs, the bolometric detector arrays, the readout, the cryogenics, and calibration strategy. Section 5 gives a detailed analysis of the statistical and systematic uncertainties in the tensor-to-scalar ratio measurement; this section also includes an analysis of the impact of foregrounds and instrumental uncertainties. Section 6 describes the scientific outcomes of *LiteBIRD* beyond the detection of primordial gravitational waves, including measurement of the optical depth to reionization, determination of neutrino masses, a search for cosmic birefringence, mapping hot gas in the Universe, a search for anisotropic CMB spectral distortions, a probe of primordial magnetic fields, and measurements to elucidate the astrophysics of the Milky Way. Section 7 describes possible extensions to the *LiteBIRD* mission design, including extending the frequency range, as well as synergy with other cosmology and astrophysics projects. Section 8 concludes this review.

# 2. CMB *B*-modes as tests of cosmic inflation

## 2.1. CMB polarization power spectra

*LiteBIRD* will provide maps of the temperature and polarization anisotropies in 15 frequency bands from 34 to 448 GHz. Fundamental theory does not predict the detailed structure of the maps, only their statistical properties, like the expected correlations between temperature and polarization anisotropies between different points on the sky. Earlier measurements by *WMAP* and *Planck* imply that the anisotropies are nearly Gaussian so that their statistical properties are predominantly characterized by the two-point correlation functions [62–65]. The observa-

<footnote n="2">²A measurement is cosmic-variance limited if the error bar is limited only by the fraction of sky available for the cosmological analysis and can no longer be decreased by improving the instrument [53–56].</footnote>
tions by WMAP and Planck also tightly constrain departures from statistical isotropy [66–69]. Under the assumption that the underlying probability distribution is isotropic, the correlations between anisotropies at different points in the sky only depend on the angle between them.

Given these properties, it is natural to consider angular correlation functions that measure the correlations between different points in the sky as a function of this angular separation. While it would be possible to work with maps and their angular correlation functions, in practice it is more convenient to expand the temperature T maps in terms of spherical harmonics,

$$ \Delta T(\hat{n}) = \sum_{\ell,m} a_{\ell m}^{T} Y_{\ell m}(\hat{n}), \qquad (1) $$

and work with the coefficients of this expansion $a_{\ell m}^T$, referred to as multipole coefficients.

Similarly, it is convenient to expand the maps of the Stokes Q and U parameters, which characterize the linear polarization, in terms of spin-weighted spherical harmonics, $_2Y_{\ell m}$,

$$ Q(\hat{n}) + iU(\hat{n}) = - \sum_{\ell,m} (a_{\ell m}^{E} + ia_{\ell m}^{B}) {}_2Y_{\ell m}(\hat{n}), \qquad (2) $$

and work with the expansion coefficients $a_{\ell m}^E$ and $a_{\ell m}^B$. This decomposition into E- and B-mode polarization is convenient because E- and B-mode patterns have distinct parity; i.e., they transform differently under the inversion of spherical coordinates, $\hat{n} \to -\hat{n}$. Specifically, the spherical harmonics coefficients transform as $a_{\ell m}^E \to (-1)^\ell a_{\ell m}^E$ and $a_{\ell m}^B \to (-1)^{\ell+1} a_{\ell m}^B$. As a result, when forming the angular power spectra<fnref n="3" />

$$ C_{\ell}^{XY} = \frac{1}{2\ell + 1} \sum_{m} a_{\ell m}^{X} a_{\ell m}^{Y*}, \qquad (3) $$

where X and Y are either T, E, or B, there are “parity-even” combinations such as $C_{\ell}^{TT}$, $C_{\ell}^{TE}$, $C_{\ell}^{EE}$, and $C_{\ell}^{BB}$ that do not change sign under the inversion of spherical coordinates, as well as “parity-odd” combinations such as $C_{\ell}^{TB}$ and $C_{\ell}^{EB}$ that do change sign. All of the parity-even combinations from the density fluctuations (scalar perturbation) have been measured already, as seen in Fig. 1, whereas $C_{\ell}^{BB}$ from the primordial gravitational waves (tensor perturbation), the target of the LiteBIRD mission, have not been detected yet [10,13,41,72]. The parity-odd combinations of the CMB polarization can be used to probe new physics that violates parity symmetry [73–77]. While no significant evidence for parity-odd power spectra of the CMB has been found (see Refs. [78–80] for summaries), $C_{\ell}^{TB}$ from the polarized dust emission in our Galaxy has been found [60,78].

As we briefly mentioned in the introduction, the decomposition into E- and B-modes is also convenient because, to linear order, the well-measured density perturbations only generate temperature and E-mode anisotropies, whereas gravitational waves lead to B-modes in addition to temperature anisotropies and E-modes. Somewhat heuristically, this can be understood from the fact that E-modes behave much like the gradient component of a vector field, whereas the B-modes behave like the curl-like component. At linear order, one can construct a gradient component from density perturbations, but it is impossible to construct a curl-component. For

<footnote n="3">³The use of angular power spectra rather than correlation functions is convenient because it leads to a nearly diagonal covariance matrix. For a non-expert review of the physics of the CMB and CMB observables see, e.g., Ref. [70] and for a more technical overview of CMB polarization see Ref. [71]. The expressions given here are idealized. In practice, foreground emission near the Galactic plane is too bright and must be masked, the instrument has finite resolution, the maps are pixelized, and so on, all of which lead to (known) corrections to these expressions.</footnote>
more details, we refer the interested reader to Refs. [30,81]. So B-modes provide the cleanest way for CMB experiments to search for primordial gravitational waves.

To see more explicitly how the information about the very early Universe is encoded, note that the contributions of primordial density perturbations to the angular power spectra of temperature or E-mode anisotropies are schematically given by

$$C_{(s),\ell}^{XX} = \int \frac{dk}{k} \Delta_{\zeta}^{2}(k) \left| \int_{0}^{\tau_0} d\tau S_{(s)}^{X}(k, \tau) j_{\ell}[k(\tau_0 - \tau)] \right|^2, \quad (4)$$

where k is the wavenumber of a Fourier mode and τ is the so-called conformal time, which is related to the physical time t as $d\tau = dt/a(t)$ with $a(t)$ being the scale factor for the homogeneous and isotropic expansion of space. The subscript “0” indicates the present-day epoch. The integrand factorizes into three pieces:

* The primordial power spectrum of density perturbations as a function of k (or equivalently radians per distance), $\Delta_{\zeta}^{2}(k)$, which contains information about the very early Universe.

* The source functions, $S_{(s)}^{X}(k, \tau)$, which contain information about the physics of the medium, largely from recombination to the present.

* The spherical Bessel functions, $j_{\ell}(x)$, for a spatially flat universe.

Similarly, the contributions of primordial gravitational waves to the angular power spectra of temperature, E-mode, and B-mode anisotropies are given by

$$C_{(t),\ell}^{XX} = \int \frac{dk}{k} \Delta_h^2(k) \left| \int_0^{\tau_0} d\tau S_{(t)}^X(k, \tau) \chi_{\ell}^X[k(\tau_0 - \tau)] \right|^2, \quad (5)$$

where $\Delta_h^2(k)$ is now the primordial power spectrum of gravitational waves, $S_{(t)}^X(k, \tau)$ are source functions for tensor perturbations in the medium, and $\chi_{\ell}^X(x)$ is a function of the spherical Bessel functions and their derivatives appropriate for $X = T, E$, or $B$ [29,35,82,83].

A wealth of information about the Universe is contained in the dependence of the source functions and the argument of the spherical Bessel function on cosmological parameters, like the matter density, the number of relativistic degrees of freedom, and so on. Here we are most interested in the information contained in the primordial power spectra, $\Delta_{\zeta}^{2}(k)$ and $\Delta_{h}^{2}(k)$, which are conventionally parametrized as [84]

$$\Delta_{\zeta}^{2}(k) = \Delta_{\zeta}^{2} \left(\frac{k}{k_{*}}\right)^{n_{s}(k)-1} \quad \text{and} \quad \Delta_{h}^{2}(k) = \Delta_{h}^{2} \left(\frac{k}{k_{*}}\right)^{n_{t}(k)}, \quad (6)$$

where $k_*$ is a pivot scale that will be taken to be $k_* = 0.05 \text{ Mpc}^{-1}$ throughout this document, and $n_s$ and $n_t$ are referred to as the scalar and tensor spectral indices, respectively. In general $n_s$ and $n_t$ are functions of k. However, the scale dependence is expected to be weak, and the default analyses typically report $n_s = n_s(k_*)$. So-called “scale-invariant” spectra correspond to $n_s = 1$ and $n_t = 0$.

Unfortunately,<fnref n="4" /> B-modes are not only generated by primordial gravitational waves, but also by weak lensing of the CMB by matter along the line of sight, which converts E-modes into B-modes [37], and by polarized Galactic emission from interstellar dust grains and relativistic electrons [38–40]. As a consequence, in order to detect the B-modes from primordial gravitational waves, both lensing and foreground contributions must be carefully accounted for. As we

<footnote n="4">⁴For the prospect of detecting primordial B-modes.</footnote>
will discuss in more detail, LiteBIRD employs 15 frequency bands to characterize and remove the foreground emission. The weak lensing signal has the same frequency dependence as the gravitational wave signal, but its angular dependence is theoretically well understood. Furthermore, because the weak lensing is caused by large-scale structure along the line of sight, some of the weak lensing signal can be removed by combining LiteBIRD with other data sets [85–89].

The theoretical predictions and current measurements of the angular power spectra are shown in Fig. 1. The LiteBIRD error bars, which are used for the constraints presented in the next sections, include foreground residuals as detailed in Sect. 5.

## 2.2. Cosmic inflation

The remarkable insight gained from analyzing cosmological data is that all cosmic structures, such as galaxies, stars, planets, and eventually us, appear to have originated from tiny quantum fluctuations in the early Universe. Within this inflationary picture, there was a very early period of nearly exponential expansion that generated the seed fluctuations for today’s structure.

According to general relativity, spacetime expands exponentially if the energy budget is dominated by vacuum energy. However, from our existence, we know that this early period of cosmological inflation must have ended. This requires a clock, or more formally a scalar field, that keeps track of time and eventually causes inflation to end. Within quantum mechanics, this scalar field will experience quantum fluctuations, and according to cosmic inflation these initially microscopic quantum fluctuations were stretched to macroscopic scales by the nearly exponential expansion, serving as the seeds of structure formation [20–24].

In this scenario, the matter sector must include a scalar field, the “inflaton”, $\phi$. For the simplest models of inflation, the action contains

$$ \int d^4 x \sqrt{-g} \left[ -\frac{1}{2} g^{\mu\nu} \partial_{\mu} \phi \partial_{\nu} \phi - V(\phi) \right], \qquad (7) $$

and is characterized by the potential $V(\phi)$. As usual, we denote the expansion rate of the Universe (called the “Hubble rate”) by $H = \dot{a}/a$, where $a(t)$ is the scale factor appearing in the Friedmann–Lemaître–Robertson–Walker (FLRW) line element. For a flat FLRW universe this line element is $ds^2 = -dt^2 + a^2(t)d\mathbf{x}^2$, and the dynamics of the scale factor is governed by the Friedman equation

$$ H^2 = \frac{8\pi G}{3} \rho, \qquad (8) $$

where $\rho = \frac{1}{2}\dot{\phi}^2 + V(\phi)$ is the energy density in the inflaton.

The slow-roll parameter $\epsilon$, the fractional rate of change of the expansion rate in one Hubble time $(1/H)$, is given by [84]

$$ \epsilon \equiv -\frac{\dot{H}}{H^2} = \frac{3\dot{\phi}^2}{\dot{\phi}^2 + 2V(\phi)}. \qquad (9) $$

If the energy density of the scalar field is dominated by the potential energy density $\dot{\phi}^2 \ll V(\phi)$, the slow-roll parameter is small, $\epsilon \ll 1$. In this case the scale factor grows nearly exponentially. To be phenomenologically viable, inflation must last sufficiently long to solve the horizon and flatness problems [16]. The simplest way to satisfy this requirement is to have a potential that is flat enough so that the fractional rate of change of the inflaton velocity per Hubble time is small. Such models of inflation, based on a single slowly rolling scalar field, predict statistically homogeneous and isotropic, adiabatic, and nearly Gaussian primordial density perturbations
with a spectrum of primordial density perturbations given by [84]

$$ \Delta_{\zeta}^{2}(k) = \frac{1}{2\epsilon M_{\mathrm{P}}^{2}} \left(\frac{H}{2\pi}\right)^{2}, \qquad (10) $$

where the slow-roll parameter $\epsilon$ and the Hubble rate $H$ are to be evaluated at a time when $k = aH$, and $M_{\mathrm{P}}$ is the (reduced) Planck mass. Since both $\epsilon$ and $H$ are slowly varying functions of time, the spectrum is expected to be nearly (but not exactly) scale invariant $n_s \simeq 1$. Furthermore, as inflation proceeds, the Hubble rate decreases. The slow-roll parameter $\epsilon$ is small during inflation, approaches unity as inflation ends, and in the simplest models increases monotonically. Decreasing $H$ and increasing $\epsilon$ implies that the simplest models predict a red spectrum, i.e., an amplitude of the power spectrum that decreases with increasing wavenumber, corresponding to $n_s < 1$. All these predictions, including the deviation from an exactly scale-invariant spectrum, have been confirmed by CMB data from WMAP [42,90,91], the Planck satellite [92–94], and various ground-based observations [95–98].

So far we have discussed the period during which the Universe expands nearly exponentially. From the cosmos today, we know that eventually this period must have ended, and the energy density in the inflaton must have been converted to a plasma of standard-model particles. This process is referred to as “reheating” [99–101]. The details of reheating are unknown but, rather remarkably, the observational predictions only weakly depend on these details, at least for the single-field models discussed here [102–104]. The main effect on observables arises from the amount by which the Universe expands during reheating. The amount of expansion during this period affects how physical scales today are related to physical scales during inflation, or more quantitatively how long has elapsed before the end of inflation $k_* = aH$.

### 2.3. Primordial gravitational waves from cosmic inflation

Constraints on the primordial spectrum of density perturbations from observations of temperature and E-mode anisotropies provide strong evidence for the quantum mechanical origin of cosmic structure, and to many they already suggest that the early Universe underwent a period of inflation. However, extraordinary claims require extraordinary evidence.

Like the scalar field, the spacetime metric also fluctuates, and just like the fluctuations in the scalar field, the microscopic fluctuations in the spacetime metric were also stretched to macroscopic scales by the inflationary expansion. So inflation predicts a statistically homogeneous and isotropic, nearly Gaussian background of primordial gravitational waves [25,26,105]. For models based on a single slowly rolling scalar field the power spectrum is given by [84]

$$ \Delta_{h}^{2}(k) = \frac{8}{M_{\mathrm{P}}^{2}} \left(\frac{H}{2\pi}\right)^{2}, \qquad (11) $$

where $H$ is again to be evaluated when $k = aH$. Since $H$ is a slowly decreasing function of time, the primordial gravitational wave spectrum is expected to be nearly scale invariant ($n_t \simeq 0$) and red ($n_t < 0$). According to Eq. (11), in the context of inflation a detection of a primordial gravitational wave signal would allow a determination of the expansion rate of the Universe during inflation. In single-field slow-roll models, the expansion rate is directly related to the energy scale of inflation, $V \simeq 3H^2 M_{\mathrm{P}}^2$.

These gravitational waves are a remarkable prediction of inflation, and their detection would provide strong independent evidence for inflation, arguably providing definitive confirmation.
A detection of this signal would also be the first observation of quantum fluctuations of space-time itself, and have other important implications to be discussed below.

## 2.4. Implications of LiteBIRD power spectrum measurements for inflation

To discuss the implications of LiteBIRD’s B-mode power spectrum measurements for inflation, it is convenient to introduce the ratio of the power in primordial gravitational waves, given in Eq. (11), to the power in primordial density perturbations, defined in Eq. (10), referred to as the “tensor-to-scalar ratio”:

$$r = \frac{\Delta_h^2(k)}{\Delta_\zeta^2(k)}. \qquad (12)$$

Key quantities like the energy scale of inflation and the range traveled by the scalar field are closely related to this parameter, and different classes of models of inflation make different predictions for $r$.

In single-field slow-roll models, the amplitude of the primordial density perturbations inferred from measurements of temperature and E-mode perturbations, together with the Friedmann equation, allows us to express the energy scale of inflation in terms of $r$ through

$$V^{1/4} = 1.04 \times 10^{16} \text{ GeV} \left(\frac{r}{0.01}\right)^{1/4}. \qquad (13)$$

Thus, a detection achievable by LiteBIRD would imply that the inflationary energy scale is close to that associated with grand unified theories, and would provide additional evidence for the idea of grand unification [31].

Under the same assumptions, the tensor-to-scalar ratio not only constrains the energy scale of inflation, but also the distance traveled by the inflaton [31],

$$\frac{\Delta\phi}{M_P} \gtrsim \left(\frac{r}{8}\right)^{1/2} N_*, \qquad (14)$$

where $N_*$ represents the number of “e-folds”, the natural logarithm of the change in linear scale of the Universe, between the time when $k_* = aH$ and the end of inflation. As briefly discussed earlier, the exact time when $k_* = aH$, and hence the value of $N_*$, depends on the details of reheating, the process that converts the energy density in the inflaton into a hot plasma of standard-model particles. This process is not well constrained, but taking $N_* = 30$ as a conservative lower limit, we see that a detection of gravitational waves above $r = 0.01$ would imply an excursion in field space that exceeds $M_P$. Such a detection would significantly constrain theories of quantum gravity, such as superstring theories (see, e.g., Ref. [106] and references therein).

In the absence of a detection, LiteBIRD will set an upper limit of $r < 0.002$ at 95% CL (accounting for both statistical and systematic uncertainties). Since both the energy scale and the field range vary slowly with $r$, an upper limit does not immediately translate into stringent constraints on either the energy scale or the distance traveled by the inflaton. To explain the implications of an upper limit and to understand the motivation for the LiteBIRD design sensitivity we will require an additional concept, that of the characteristic scale of the potential [59,107]. To introduce this quantity and highlight its importance, we will begin with an argument that does not involve the microscopic details of a particular model of inflation.

Provided the fractional rate of change of the expansion rate is small compared to the expansion rate, $\epsilon \ll 1$, the tensor-to-scalar ratio $r$ obeys a simple differential equation in terms of the
number of e-folds N until the end of inflation [108–110]:

$$ \frac{d \ln r}{dN} = [n_s(N) - 1] + \frac{r}{8}. \qquad (15) $$

The cosmic microwave background allows us to observe a window of a few e-folds around $N_*$, which we typically expect to be between 50 and 60. The observed departure of the primordial power spectrum from scale invariance is numerically close to $(p+1)/N_*$, where p is some number of order unity. In the simplest models of inflation, we expect additional small or large numbers beyond $N_*$ to be absent, which means that we expect $n_s(N) - 1 = -(p+1)/N$. In this case, we can solve the differential equation and find the general solution up to an integration constant $N_{eq}$. If we continue with the assumption that there are no additional large or small numbers, the solution is well described by one of two limiting behaviors,

$$ r(N) = \frac{8p}{N} \quad \text{and} \quad r(N) = \frac{8p}{N} \left( \frac{N_{\text{eq}}}{N} \right)^p, \qquad (16) $$

where p is constrained to be positive, consistent with the observed red spectrum $n_s < 1$ [42,92], and by assumption $N_{eq}$ is expected to be of order unity.

We previously saw that the simplest single-field models are completely characterized by a potential. It is then natural to ask which potentials give rise to these solutions. It can be shown that the first solution in Eq. (16) corresponds to potentials that at least during inflation are well approximated by a monomial $V(\phi) \simeq \mu^{4-2p}\phi^{2p}$. For p of order unity, we see that this class of models predicts $r \gtrsim 0.01$, which is easily within reach of LiteBIRD.

For the second solution, the qualitative behavior depends on the value of p. For $p > 1$ the potential corresponds to so-called “hilltop” inflation models [111] for which the potential near the origin in field space approaches a constant from below like a power of the field set by p. Inflation occurs as the field rolls off the hill toward a minimum at larger field values. For $p < 1$ the potentials correspond to so-called “plateau” models, for which the potential approaches a constant from below at large field values, again with a power set by p. In this case inflation occurs as the field rolls off the plateau toward a minimum near the origin.

Rather intriguingly, the current measurement of $n_s$ favors $p \simeq 1$, which is a special case. It corresponds to plateau models in which the plateau is approached exponentially:

$$ V(\phi) \simeq V_0 (1 - e^{-\phi/M}) . \qquad (17) $$

This behavior occurs in many models of inflation, including the Starobinsky $R^2$ model for inflation [14] (discussed in more detail below), models in which inflation is driven by the Higgs boson [112,113], or more generally models with a non-minimally coupled inflaton [114], fiber inflation [115], Poincaré disk models [116,117], α-attractors more generally [93,118–120], or the Goncharov–Linde model [121,122], to name just a few.

The “characteristic scale of the potential” $M$ is related to the integration constant $N_{eq}$ according to $M = \sqrt{N_{eq}} M_P$. This allows us to express the tensor-to-scalar ratio in this class of models in terms of the characteristic scale as

$$ r \simeq 0.0025 \left( \frac{57}{N_*} \right)^2 \left( \frac{M}{M_P} \right)^2. \qquad (18) $$

Instantaneous reheating corresponds to $N_* \simeq 57$. Any delay in reheating will decrease $N_*$, and hence will increase the expected tensor-to-scalar ratio for a given characteristic scale. As a consequence, for $M \gtrsim M_P$ we expect $r \gtrsim 0.0025$, so that an upper limit from LiteBIRD with $r < 0.002$ at 95% CL (accounting for both statistical and systematic uncertainties) would disfavor
<figure><img src="image_3.png" /><figcaption>**Fig. 2.** LiteBIRD constraints on the tensor-to-scalar ratio $r$ and the scalar spectral index $n_s$ assuming Starobinsky's $R^2$ model for inflation [14] with $N_*=51$ (specifically the analytic prediction described in the text) as the fiducial model. The lighter and darker green regions show 68% and 95% confidence-level limits achievable with LiteBIRD and Planck. The lighter and darker orange regions (partly hidden behind the green regions) show 68% and 95% confidence-level limits achievable with LiteBIRD alone. The current limits are shown in light blue. The dotted blue lines show representative cases of the first class of models described in the text, monomial models. The red line and the dark purple dot show the predictions of the Starobinsky model [14] (labeled as $R^2$) and models that invoke the Higgs field as the inflaton [112,113], respectively. The light purple lines show the prediction for Poincaré disk models [116,117].</figcaption></figure>

any of the simplest models of inflation with a characteristic scale of the potential larger than the Planck scale.

In models such as the Starobinsky model, the Planck scale does not occur by accident, but appears because the characteristic scale and the Planck scale are set by the same dimensionful coefficient in the action, the coefficient of the Einstein-Hilbert term. This makes models with $M \gtrsim M_P$ a natural target for LiteBIRD. In Fig. 2 we take the Starobinsky model as our fiducial model to showcase what a detection of primordial gravitational waves with LiteBIRD would look like in the $n_s-r$ plane.

For a given reheating history, a model makes a definitive prediction, corresponding to a point in the $n_s-r$ plane. However, since the reheating history is uncertain, we represent the predictions of models by bars corresponding to $47 < N_* < 57$. One exception to this general rule is the Starobinsky model. Unlike for most models, the underlying idea of this example is that inflation is a consequence of a short-distance modification of the theory of gravity rather than a consequence of the matter sector. Even though the Starobinsky model can be written as a scalar-tensor theory, like any generic $f(R)$ theory [123,124], this idea naturally predicts that the couplings to matter fields responsible for reheating are gravitational couplings in the $f(R)$ frame. In this case, reheating is somewhat delayed. More detailed studies suggest that the delay corresponds to a change in $N_*$ of about 5. Thus, we take $N_* = 51$ for our fiducial model. In our simple analytic approximation, this leads to $r \simeq 0.0046$ and $n_s \simeq 0.961$. Since reheating is expected to be slower, but the details are uncertain in the Starobinsky model as well, we show the model prediction with $42 < N_* < 52$. The second exception to the rule are models in which the inflaton is identified with the Higgs field. In this case we know the couplings to the matter
<figure><img src="image_4.png" /><figcaption>**Fig. 3.** *LiteBIRD* constraints for a fiducial model with $r = 0$. The lighter and darker green regions show 68% and 95% confidence-level upper limits achievable with *LiteBIRD* and *Planck*. The lighter and darker orange regions (partly hidden behind the green regions) show 68% and 95% confidence-level upper limits achievable with *LiteBIRD* alone. The blue band shows the first class of models mentioned in the text, monomial models. The gray band shows a concrete representative second class of plateau models with $p = 1$, $\alpha$-attractors [118]. As discussed in the text, the second class of models depends on the characteristic scale of the potential $M$. The darker gray lines show $\alpha$-attractors with $M = M_P$ and $M = 5M_P$. In the absence of a detection, *LiteBIRD* will exclude the first class of models at high significance, and will exclude models in the second class with a super-Planckian characteristic scale, which includes the Starobinsky model [14] and models that invoke the Higgs field as the inflaton [112,113], shown as the red line and the purple dot, respectively.</figcaption></figure>

fields, and the reheating history is calculable. To reflect this, we represent these models by a single point in the $n_s-r$ plane at $N_* = 57$, even though some uncertainty exists here as well.

Among the examples given above, the Goncharov–Linde model [121,122] predicts a sub-Planckian characteristic scale, and $\alpha$-attractors [93,118–120] with a sub-Planckian characteristic scale also exist. So a detection of primordial gravitational waves with *LiteBIRD* is by no means guaranteed. We thus also showcase what an upper limit would look like in Fig. 3. Let us note that in addition to being simpler in the sense that they do not contain a large hierarchy of scales, models with $M \gtrsim M_P$ are also simpler in a different sense. One may ask whether inflation will begin for general initial conditions for a given model, and it has recently become possible to investigate this question in numerical general relativity, assuming that the description in terms of a single scalar field is already appropriate at that time [125–128]. The simulations show that models with $M \gtrsim M_P$ are significantly more robust to inhomogeneities than those with $M < M_P$ [128]. This does not imply that inflation cannot begin in models with a sub-Planckian characteristic scale, but it does suggest that additional dynamics (which could simply be in the form of another field) is needed to set up initial conditions that are appropriate for inflation to begin in such models. So an upper limit from *LiteBIRD* would disfavor the simplest models of inflation that naturally predict the observed value of $n_s$ and would also be a milestone for early Universe cosmology that provides key information about the inner workings of the earliest moments of the cosmos.
## 2.5. *Beyond the B-mode power spectrum*

Single-field slow-roll inflation predicts a stochastic background of gravitational waves that originated from quantum vacuum fluctuations in spacetime and is nearly scale invariant, nearly Gaussian, and parity conserving [25,26,105]. The detection of a violation of any of these properties would point to new physics beyond the simplest models of inflation [129]. The first condition can be tested by reconstructing the power spectrum $\Delta_h^2(k)$ from the observed B-mode power spectrum [130,131], the second property can be tested through measurements of the three-point function (bispectrum) [132–135], and the third property can be tested by parity-violating correlation functions such as the cross-correlation between the temperature and the B-mode polarization, between the E- and B-mode polarizations [73,76,77,136,137], or parity-violating contributions to the three-point function [138].

These conditions can be violated when non-minimal couplings of the inflaton are present [73,139,140], or when other fields are present during inflation and source gravitational waves. The energy density in these fields must be sub-dominant compared to the energy density in the inflaton. However, their energy density may still be sufficient to produce gravitational waves with an amplitude within reach of *LiteBIRD*.

The additional sources could be scalar fields [141–144], a U(1) gauge field [136,145–149], or an SU(2) gauge field [150–157]. All these sources can produce strongly scale-dependent gravitational waves (and, in general, density perturbations) that are highly non-Gaussian. The latter two types of source can produce parity-violating gravitational waves. Hence a stochastic gravitational wave background generated during inflation need not satisfy any of the conditions predicted by single-field slow-roll inflation. If the gravitational waves sourced by the matter fields dominate over the vacuum fluctuations in the metric, then detecting B-mode polarization from primordial gravitational waves no longer generally implies the discovery of the quantum nature of space (although the matter that created them was still produced quantum mechanically). Nevertheless, such a discovery would still provide definitive evidence for inflation because we need inflation to stretch the wavelengths of gravitational waves to billions of light years.

An example of a U(1) gauge field is the primordial magnetic field, which can source tensor perturbations that are non-scale invariant, non-Gaussian, and parity violating (see Ref. [138] and references therein). Magnetic fields can also induce a spatially dependent rotation of polarization angles of the CMB by means of Faraday rotation. The effect can be detected using multi-frequency data because the Faraday rotation angle is inversely proportional to the square of the frequency. We discuss this possibility further in Sect. 6.5.

The axion–SU(2) model described in Ref. [157] provides an example that illustrates the benefits of a satellite mission with full sky coverage and access to the reionization bump. This model contains the inflaton, an axion, and SU(2) gauge fields. The energy density is always dominated by the inflaton field. The axion field $\chi$ has a potential of the form $V(\chi)\propto 1 + \cos(\chi/f)$, where $f$ is the axion decay constant, and the axion is coupled to the gauge fields through a Chern–Simons term, $\chi F \tilde{F}$. For time-dependent $\chi$, one of the helicities of the gauge field is amplified. This produces chiral gravitational waves [152,154,158] with parity-violating correlations in the CMB power spectra and circular polarization for laser interferometers [137]. The shape of the tensor power spectrum is determined by the evolution of $\chi$ during inflation, and hence by the shape of $V(\chi)$. For the cosine potential, the axion velocity increases initially, reaches the maximum at the inflection point, $\chi(t_*) = \pi f/2$, and then decreases. The resulting tensor power spectrum
<figure><img src="image_5.png" /><figcaption>Fig. 4. B-mode power spectra, $D_{\ell} = \ell(\ell + 1)C_{\ell}^{BB}/2\pi$, for the Starobinsky model with $r = 0.00461$ and $n_t = -r/8$ (black dotted line) and for axion-SU(2) inflation with two sets of parameters (see Eq. (19) for the definition): one with $r_* = 0.00461$, $k_p = 0.01$ Mpc$^{-1}$, and $\sigma = 1$ (purple dashed line) and another with $r_* = 0.041$, $k_p = 9 \times 10^{-6}$ Mpc$^{-1}$, and $\sigma = 3.2$ (orange dot-dashed line). The tensor-to-scalar ratio of the vacuum fluctuations is chosen to be $r_{vac} = 10^{-4}$. The cosmic-variance-only (including primordial and lensing B-mode variance) and total LiteBIRD $\pm 1\sigma$ error bars (including foreground residuals) are shown as the gray and blue regions, respectively.</figcaption></figure>

is approximately log-normal [137,159],

$$ \Delta_{h \text{L, sourced}}^2(k) = r_{*, \text{sourced}} \Delta_{\zeta}^2(k) \exp \left( -\frac{1}{2\sigma^2} \left[ \ln \left( \frac{k}{k_p} \right) \right]^2 \right), \quad (19) $$

where $r_{*, \text{sourced}}$ (hereafter $r_*$) and $k_p$ are the tensor-to-scalar ratio and the wavenumber at the maximum, and $\sigma^2$ is the width of the power spectrum. The subscript “L” (for “left”) stands for one of the polarization states (determined by the sign of $\dot{\chi}$), while the other polarization state is not amplified and is negligible. These quantities are determined by the parameters of the model [137,159,160]. This sourced contribution is added to the vacuum contribution characterized by the vacuum tensor-to-scalar ratio, $r_{vac}$. The self-interaction of the gauge fields leads to non-Gaussian gravitational waves [133–135].

In Fig. 4, we compare example B-mode power spectra of this model (dot-dashed and dashed lines) and that of the Starobinsky model (dotted line). The parameters are chosen such that they all have indistinguishable recombination bumps ($\ell \simeq 80$), whereas they are very different in their reionization bumps ($\ell \simeq 4$). Therefore, a full-sky survey enabled by a space mission such as LiteBIRD is necessary for establishing the origin of the primordial gravitational waves: tensor vacuum fluctuation versus sourced gravitational waves.

We conclude that, in the case of a detection, it will be important to confirm the detailed predictions of single-field slow-roll models using the LiteBIRD data before claiming discovery of the quantum nature of spacetime. Applying the established methodology for the CMB
bispectrum estimation to the *LiteBIRD* B-mode data will allow us to improve constraints on tensor non-Gaussianities by several orders of magnitude [138]. A violation of any of the basic predictions of single-field slow-roll models of inflation for gravitational waves (i.e., nearly scale invariant, nearly Gaussian, parity conserving) would have profound implications for our understanding of the dynamics of inflation.

## 2.6. The need for measurements from space

The COBE, WMAP, and Planck data sets are recognized as the reference experiments for their respective CMB science goals. The success of these experiments depended on the advantages of the space environment for making high-fidelity observations of the CMB. These advantages include the following.

* All frequencies are accessible, unlike on the ground where water and oxygen lines block access and reduce the ability to build a detailed model of the foreground emission. In particular, space observations can measure frequencies far into the Wien tail of the CMB to distinguish CMB fluctuations from Galactic dust emission.

* Detector sensitivity is higher in space than on the ground due to the absence of atmospheric loading and the disparity increases rapidly with frequency, giving much better per-detector leverage on Galactic dust measurements from space. As a rule of thumb, one detector in space is equivalent to 100 detectors (of the same quality) on the ground.

* The absence of atmospheric emission and its large brightness fluctuations in space-based measurements give high-fidelity maps on large angular scales corresponding to $2 \le l \le 30$.

* Bright sources such as the Earth and Sun are kept far from the boresight of the telescope by a large angle, giving very low systematic errors due to pickup of those sources in the telescope sidelobes.

*LiteBIRD*'s ability to measure the entire sky at the largest angular scales with 15 frequency bands is complementary to that of ground-based experiments, which will focus on deep observations of low-foreground sky to search for an inflationary signal. *LiteBIRD* observations have the potential to detect *both* the recombination peak at $l \approx 80$ and the reionization peak at $l \approx 4$. As highlighted earlier, high significance detections of both peaks would provide firm evidence that we have detected the signature of inflation. A primary science requirement for *LiteBIRD* is to detect both peaks with greater than 5 σ significance for a relatively high value of $r=0.01$. Detection of both peaks is necessary to distinguish between cosmological models with a similar recombination peak, as discussed in the previous section. For all detectable values of $r$, the all-sky data from *LiteBIRD* can be tested for isotropy, which is a critical feature of a true cosmological B-mode signal.

Finally, *LiteBIRD* can provide valuable foreground information for ground-based experiments. Ground-based experiments can improve *LiteBIRD*'s observations with high-resolution lensing data. The *LiteBIRD* data set will be timely, since it will be available at the same time as ground-based CMB data from Chile and the South Pole, as well as other powerful cosmological data sets such as those from the Vera C. Rubin Observatory, *Euclid*, and the *Nancy Grace Roman Space Telescope*.
## 2.7. Comparison with other probes

Several methods have been proposed for observing primordial gravitational waves other than through CMB polarization measurements. These include future projects for a gravitational wave interferometer [161], a technique using pulsar timing arrays [162,163], and a method using the 21-cm line [164]. The sensitivity of the CMB to primordial gravitational waves is much better than those of the other probes, assuming the spectrum expected from standard cosmology; for instance, the sensitivity of LiteBIRD is about 10 million times greater than that of LISA [160]. Therefore, the discovery of primordial gravitational waves seems dramatically more likely to come from CMB observations in this case. Once the primordial gravitational waves are discovered with CMB polarization observations, it will give us a concrete target for future projects using other methods. In some non-standard models, primordial gravitational waves can be enhanced at shorter wavelengths. Their observability by various probes including that of LiteBIRD is discussed elsewhere [160] with the conclusion that LiteBIRD is competitive even in those non-standard models.

# 3. LiteBIRD overview

## 3.1. Project overview

After some initial conceptual studies [165–169] that started in 2008, we proposed LiteBIRD in 2015 as JAXA’s large-class (L-class) mission candidate. JAXA’s L-class is for flagship science missions with a 30 billion yen cost cap. There will be three L-class missions in about ten years, launched using JAXA’s H3 rocket. LiteBIRD passed an initial down-selection and completed a two-year Pre-Phase-A2 concept development phase in 2018. JAXA selected LiteBIRD in May 2019 as the second L-class mission after MMX, the Martian Moons Exploration, which will be launched in the mid-2020s.

The LiteBIRD Collaboration has more than 300 researchers as of January 2022, based in Japan, North America, and Europe, with experience in CMB experiments, X-ray satellite missions, and other large projects in high-energy physics and astronomy. In particular, a large number of researchers who worked on the Planck satellite are members of LiteBIRD. We thus consider LiteBIRD to be the successor to the Planck satellite.

LiteBIRD will survey the polarization of the CMB radiation over the full sky with unprecedented precision. The full success criterion of LiteBIRD is to achieve $\delta r < 0.001$ for a fiducial model with $r = 0$, where $\delta r$ is the total error on the tensor-to-scalar ratio.

Specifically, we define this as the value covering the 68% area of the posterior probability function for $r$:

$$ \frac{\int_{0}^{\delta r} L(r)dr}{\int_{0}^{\infty} L(r)dr} = 0.68. \qquad (20) $$

The posterior, $L(r)$, including both statistical and systematic components, will be described in Sect. 5.

This section gives a concise overview of LiteBIRD. In Sect. 3.2, we describe our Level-1 mission requirements, or scientific requirements, and the rationale behind them. In Sect. 3.3, we introduce our measurement requirements and their flow down to system requirements. After describing the launch vehicle (Sect. 3.4), we introduce the spacecraft and the payload module (Sect. 3.5), the service module (Sect. 3.6), and the operation concept (Sect. 3.7.)
<table><caption>**Table 1.** The two basic science requirements for *LiteBIRD*, also called Level-1 (Lv1) mission requirements.</caption><thead><tr><td>ID</td><td>Title</td><td>Requirement description</td></tr></thead><tbody><tr><td>Lv1.01</td><td>Tensor-to-scalar ratio r<br>measurement sensitivity</td><td>The mission shall measure r with a total uncertainty of δr &lt; 1 × 10<sup>-3</sup>. This value shall include contributions from instrumental statistical noise fluctuations, instrumental systematics, residual foregrounds, lensing B-modes, and observer bias, and shall not rely on future external data sets.</td></tr><tr><td>Lv1.02</td><td>Polarization angular power spectrum<br>measurement capability</td><td>The mission shall obtain full-sky CMB linear polarization maps for achieving &gt; 5 σ significance using 2 ≤ ℓ ≤ 10 and 11 ≤ ℓ ≤ 200 separately, assuming r = 0.01. We adopt a fiducial optical depth of τ = 0.05 for this calculation.</td></tr></tbody></table>

## 3.2. *Science requirements*

In Fig. 1 (Sect. 2 above), we summarized the present measurements of the CMB power spectra, including B-modes, with the expected polarization sensitivities of *LiteBIRD* displayed. The B-mode power is proportional to the tensor-to-scalar ratio, *r*, which has been observationally constrained by BICEP/Keck to be *r* < 0.036 (95% CL) [12], with a recent update folding in a re-analysis of Planck data yielding *r* < 0.032 (95% CL) [72,170] and *r* < 0.037 (95% CL) [171]. The next generation of CMB polarization experiments on the ground have the potential to observe the signal around *ℓ* ≃ 80, coming from the recombination epoch. However, if *r* is less than approximately 0.03, the B-modes due to gravitational lensing become dominant. Removing contamination of the lensing B-modes, often called “delensing”, is needed in this case. In contrast, the other primordial signal, at *ℓ* < 10, which is due to reionization, is larger than the lensing B-modes, even for *r* = 0.001. In order to access the reionization peak, one needs to survey the full sky, where the advantage of observing in space is clear.

The critical question is: to what precision should *r* be measured? Here we introduce the total uncertainty on *r*, δ*r*, which consists of five components: (instrumental) statistical uncertainties; systematic uncertainties; uncertainties due to contamination of foreground components; uncertainties due to gravitational lensing; and uncertainties due to observer biases. There are many different inflationary models under active discussion, which predict different values of *r*. Among them, there are well-motivated inflationary models that predict *r* > 0.01 [30]. If our requirement is δ*r* < 0.001, we can provide more than 10 σ detection significance for such models. On the other hand, if *LiteBIRD* finds no primordial B-modes and obtains an upper limit on *r*, then this limit will be stringent enough to set severe constraints on the physics of inflation. As discussed in Sect. 2.4, if we obtain an upper limit at *r* ~ 0.002, we can completely rule out one important category of models, namely any single-field model in which the characteristic field-variation scale of the inflaton potential is greater than the reduced Planck mass.

Based on all the considerations described above, we decided to impose the requirements described in Table 1. The first, Lv1.01, shall be achieved *without* delensing using external data; if external data are available, we may further reduce δ*r* [172]. The second requirement, Lv1.02, is essential to cover the case where *r* turns out to be large. If there are already indications of the primordial B-modes before the observations by *LiteBIRD*, that would imply a relatively large value of *r*. In this case, data from *LiteBIRD* will allow us to measure the B-mode signals from reionization and recombination simultaneously. If the spectral shape is consistent with
<table><caption>**Table 2.** Definitions of five requirement levels used in LiteBIRD's requirements flow down. We split the requirements into five levels, from the top-level science requirements (Lv1) to (instrumental) unit requirements (Lv5). Each level is allowed to have a sub-structure; e.g., a Level-2 requirement Lv2.01 has six sub-requirements (Lv2.01.01, Lv2.01.02,...).</caption><thead><tr><th>Class</th><th>Symbol</th><th>Description</th></tr></thead><tbody><tr><td>Level 1 (Lv1) science requirements</td><td> Lv1.XX (e.g., Lv1.01)</td><td>Mission requirements<br/>Top-level quantitative science requirements that are directly connected to the full success of the mission.</td></tr><tr><td>Level 2 (Lv2) measurement requirements</td><td> Lv2.XX(.YY) (e.g., Lv2.01, Lv2.01.01)</td><td>Measurement requirements to achieve Lv1.<br/>No assumption is made on an instrument.</td></tr><tr><td colspan="3" style="text-align: center;">↓↓<br/>Implementation trade-off studies</td></tr><tr><td>Level 3 (Lv3) integrated system requirements</td><td> Lv3.XX(.YY) (e.g., Lv3.01, Lv3.01.01)</td><td>↓↓<br/>System requirements<br/>Top-level implementation requirements for a chosen instrument to achieve Lv2. Between Lv2 and Lv3 are trade-off studies for instrument selection.</td></tr><tr><td>Level 4 (Lv4) instrument requirements</td><td> Lv4.XX(.YY) (e.g., Lv4.01, Lv4.01.01)</td><td>Instrument requirements to achieve Lv3.</td></tr><tr><td>Level 5 (Lv5) unit requirements</td><td> Lv5.XX(.YY) (e.g., Lv5.01, Lv5.01.01)</td><td>Requirements on units composing each instrument to achieve Lv4.</td></tr></tbody></table>

expectations from the standard cosmology, that will narrow down the list of possible inflationary scenarios, and provide a much deeper insight into the correct model. If we observe an unexpected power spectrum, beyond the standard-model prediction, that will lead to a revolution in our picture of the physics of the early Universe. Lv1.02 also sets the angular resolution requirement for LiteBIRD.

### 3.3. Measurement requirements and system requirements

To satisfy the science requirements described in the previous section, we use the requirements flow-down framework shown in Table 2. To derive Lv2 measurement requirements from Lv1 science requirements, we also consider program-level constraints, such as the cost cap, which are not controlled by the LiteBIRD team. We use agreed-upon assumptions between the LiteBIRD team and other parties or within the LiteBIRD team; examples include assumptions on the complexity of the astronomical foreground components, the cooling-chain lifetime, and basic system redundancy guidelines. There are in total 11 Lv2 measurement requirements on the statistical uncertainty (Lv2.01), the systematic uncertainty (Lv2.02), the scan strategy (Lv2.03), the angular resolution (Lv2.04), calibration measurements (Lv2.05), error budget allocation (Lv2.06), systematic error budget allocation (Lv2.07), the duration of the normal observation phase (Lv2.08), the orbit (Lv2.09), observer bias (Lv2.10), and noise-covariance knowledge (Lv2.11). Our error budget (Lv2.06) is defined such that an equal amount is given to the total statistical error after foreground separation $\sigma_{stat}$ and the total systematic error $\sigma_{syst}$. The requirements that we chose are thus $\sigma_{stat} < 0.6 \times 10^{-3}$ on the statistical uncertainty (Lv2.01) and
$\sigma_{\text{syst}} < 0.6 \times 10^{-3}$ on the systematic uncertainty (Lv2.02).<fnref n="5" /> Since we assume no delensing using external data, $\sigma_{\text{stat}}$ includes uncertainties from the lensing B-mode component. Uncertainties due to foreground separation are also in $\sigma_{\text{stat}}$. The observer bias (Lv2.10) shall be much smaller than $\sigma_{\text{syst}}$. The requirement on the statistical uncertainty (Lv2.01) has six sub-requirements on: (1) CMB sensitivity; (2) dust emission; (3) synchrotron emission; (4) separation of CO lines; (5) the number of observing bands; and (6) the observing frequency range. These are determined through detailed simulation. We require full-sky surveys (Lv2.03) to obtain the B-modes to the lowest multipole of $\ell = 2$. The angular resolution (Lv2.04) shall be better than 80 arcmin full width at half maximum (FWHM) in the lowest-frequency band in order to perform precision measurements at $\ell = 200$. The regular observation phase (Lv2.08) shall be three years, considering the total cost cap and cooling-chain lifetime. The lifetime is determined by the degradation of working gas and moving parts of the mechanical coolers. The degradation is suppressed through our technology development to assure the required lifetime. The satellite shall be in a Lissajous orbit (Lv2.09) around the Sun-Earth L2 point to avoid the influence of radiation from the Sun, Moon, and Earth (discussed further in Sect. 3.7). Requirements on calibration measurements (Lv2.05, Lv2.11) and systematic error budget allocation (Lv2.07) will be explained in Sect. 4.

Lv1 and Lv2 requirements are collectively called “mission requirements”. In general, several possible designs meet mission requirements, and so we performed implementation trade-off studies to choose the best design. We also considered program-level constraints and assumptions that we used to set Lv2 requirements.

Lv3 integrated system requirements constitute top-level system requirements. An essential distinction between Lv2 and Lv3 is that Lv3 requirements are for the system chosen from trade-off studies, while Lv2 measurement requirements do not assume a specific system in principle. Lv3 requirements include general system requirements not only for mission instruments but also for the bus system,<fnref n="6" /> ground segments, and ground-support equipment. There are too many Lv3 requirements to list here. The requirement flow’s tree structure is also too detailed to show, since some Lv3 requirements derive from more than one Lv2 requirement; however, we will explain some essential Lv3 requirements in Sect. 4.

### 3.4. Launch vehicle

LiteBIRD will be launched on an H3 [173], Japan’s new flagship rocket. It will achieve greater flexibility, reliability, and performance at a lower cost than the currently used H-IIA rocket. The H3 rocket is under development through its prime contractor, Mitsubishi Heavy Industries, with a maiden flight scheduled in 2022. The first stage of the H3 rocket will adopt the newly developed liquid engine, LE-9, which achieves a thrust 1.4 times larger than the LE-7A engine currently in use. Its second-stage engine, LE-5B-3, and the solid rocket booster, SRB-3, will also be improved. The launch capability of the H3 rocket to a geostationary transfer orbit will be the highest ever among JAXA’s launch vehicles, exceeding that of the existing H-IIA and H-IIB launch vehicles. The launch facility at Tanegashima Space Center will also be upgraded following the development of H3.

<footnote n="5">⁵The requirement allows us to keep a sufficient margin to absorb additional noise penalty due to debiasing as described in Sect. 5.4.</footnote>

<footnote n="6">⁶Also called the “service module”, or “SVM” for short.</footnote>
The design of the H3 rocket allows for several different configurations. The rocket type is defined by the combination of the number of first-stage engines (2 or 3), the number of solid rocket boosters (0, 2, or 4), and the length of the fairing (short or long). These setups make it possible to cope with various payload sizes and orbits. Considering the size, weight, and orbit of *LiteBIRD*, we plan to adopt the H3-22L configuration, which means two first-stage engines, two boosters, and a long fairing. The estimated launch capability with this configuration is larger than 3.5 t. We thus set a provisional requirement on the total weight of *LiteBIRD* as < 3.5 t. This requirement may be updated after the first flight of the H3 rocket.

In most cases, the launch environment of H3 is expected to be similar to or more moderate than that of H-IIA. Details of the launch environment may depend on the rocket configuration, especially on the number of solid rocket boosters, the satellite mass, and the flight path. We conservatively assume the launch environment of H-IIA in general for the design of *LiteBIRD*. However, when the launch environment is critical in the design, such as for the mechanical requirement on the fundamental frequency of the satellite, we adopt requirements based on the current best estimation of the performance of H3.

## 3.5. *Spacecraft overview*

The overall structure of the spacecraft for *LiteBIRD* is determined directly from the mission requirements. The axisymmetric shape of the spacecraft is selected for reducing the moment of inertia to make the spin easier. We chose to place the payload module (PLM), including the telescopes, at the top of the spacecraft and the solar panels at its bottom, perpendicular to the spin axis. The high-gain antenna should be placed on the bottom side of the satellite, i.e., opposite the mission instruments, to point to the Earth and reduce interference with the telescopes. Based on these considerations, we show the basic structure of the spacecraft in Fig. 5.

In this configuration, the whole spacecraft spins, and the possibility of using a slip-ring to rotate only the PLM is *not* adopted. The main reasons for this selection are to handle large heat dissipation in the PLM and to reduce the possibility of a single-point failure. The PLM is equipped with mechanical coolers, which dissipate a fairly large amount of heat. A radiator of sufficient size to dissipate the heat can be equipped only in the service module (SVM) and it is not easy to transfer heat from the spinning PLM through the slip-ring to a non-spinning SVM. The slip-ring introduces a single point whose failure would be critical for the mission. Furthermore, a slip-ring might produce micro-vibration and could increase the detector noise significantly. For these reasons, we decided to rotate the whole spacecraft and not to adopt the slip-ring.

The spacecraft has a thrust tube at its center, which transfers the PLM launch load to the rocket. We will install the fuel tank inside the thrust tube to utilize the inner space effectively. The insides of the side panels are used to mount various electric components of both the SVM and PLM. PLM components are preferentially placed on the upper parts of the side panels, whereas SVM components are on the lower parts of the side panels. The outer sides of the upper parts of the side panels are used to mount radiators, which radiate the heat dissipated in the PLM, such as from the mechanical coolers and electronics boxes.

We show a block diagram of the spacecraft in Fig. 6. The *LiteBIRD* spacecraft uses a typical satellite configuration. Observation of the entire sky is conducted through the scan strategy that is detailed in Sect. 5.1. The slow spin rate of 0.05 rpm makes it possible to adopt three-axis attitude control that satisfies the *LiteBIRD* attitude accuracy requirements, even if the space-
<figure><img src="image_6.png" /><figcaption>**Fig. 5.** Conceptual design of the *LiteBIRD* spacecraft. The payload module (PLM) houses the low-frequency telescope (LFT), the mid-frequency telescope (MFT), and the high-frequency telescope (HFT).</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>**Fig. 6.** Block diagram of the spacecraft for *LiteBIRD*. Boxes with broken lines represent electric equipment, while those with solid lines are subsystems composed of multiple equipment types. Lines and arrows connecting boxes are only representative.</figcaption></figure>
craft spins. The spacecraft will have a total weight of 2.6 t, including the fuel of approximately 400 kg, and a total height of 5.3 m. Thus the current weight has a large margin compared to the rocket's capability. We estimate the total power of the spacecraft to be 3.0 kW. The down-link rate will be 10 Mbps in the X band and will transfer a total of 17.9 GB of scientific data every day. All these parameters are subject to change as the conceptual design of the satellite continues to be developed.

### 3.6. Service module

The service module (SVM) of *LiteBIRD* includes an attitude orbit-control system (AOCS), thermal control system, communication system, data-handling system, power system, and other subsystems. The SVM of *LiteBIRD* utilizes existing technology as much as possible to reduce the development cost and risks. In what follows, we briefly describe some characteristics of the SVM.

*LiteBIRD* is a zero-momentum, three-axis stabilized spacecraft designed to realize the required pattern of an all-sky survey, i.e., the combination of spin and precession. Momentum wheels (MWs) are used to control the attitude of the spacecraft, and the reaction control system (RCS) is used to unload the MWs and to control the orbit. Because the spacecraft is operated with zero momentum, relatively large MWs are required to cancel the angular momentum due to the spin. The MWs also cancel the spin-axis component of the angular momentum due to the polarization modulators. Other wheels are used to control the precession of the spacecraft. The spacecraft receives a small amount of external torque even at L2, mostly from solar radiation. This causes a steady increase or decrease of the rotational frequencies of the MWs, and thus the RCS is used to unload the MWs regularly. The RCS also provides the required $\Delta V$ for the initial correction of the orbit and for the orbit insertion at L2. In addition, we use the RCS once every few months to correct orbit errors, since L2 is a gravitational saddle point and any orbit around it is intrinsically unstable.

The AOCS uses star trackers (STTs) and inertial reference units (IRUs) to determine the spacecraft's attitude because a good attitude solution is required for *LiteBIRD*. The spin rate of 0.05 rpm corresponds to $0.3 \text{ deg s}^{-1}$. This spin speed is easily handled by the currently available STTs and the degradation of the attitude solution is negligible. The situation is the same for the currently available IRUs. We expect that the STTs can track stars continuously, but the IRUs will be used to interpolate the attitude in case the STTs temporarily fail to track stars.

A thermal control system keeps the temperature of the on-board components in the required range. This is not easy when some of the components have large heat dissipation or require tight temperature stability. Components with large heat dissipation are the mechanical coolers, their drivers, and the signal-processing units. Adiabatic demagnetization refrigerator controllers and SQUID controller units require tight temperature stability. The total heat dissipation of the payload module is about 1.4 kW. Because there is no room in the payload module for sufficient radiators for this amount of heat dissipation, radiators are placed on the upper parts of the side panels of the spacecraft. The total area of the radiators may be estimated to be approximately $10 \text{ m}^2$. Heat pipes may be used to transfer heat from the components to the radiators. When accurate temperature control is required, heaters are used in combination with the radiators.

*LiteBIRD* uses the X band for telemetry and command (and ranging), and also for the down-link of the mission data. The main reason to use the X band for telemetry and command is that the primary GRound station for deep space Exploration And Tele-communication (GREAT)
supports only the *X* band, not the *S* band, for uplink. We will also use the 34-m antenna at Uchi-
noura Space Center (USC) as a secondary station. Because GREAT is the only deep space
station in Japan, many interplanetary satellites will use the station. The secondary station is
useful when GREAT is unavailable due to tracking other satellites. However, the USC 34-m
antenna is smaller than GREAT (54-m antenna), and so the downlink rate at USC 34m will
be only 1/3 of that of GREAT. The required downlink rate for the mission data, 10 Mbps, will
be achieved only with GREAT. To achieve this rate, we will use a parabolic antenna with a
diameter of 0.5 m mounted on a 2D gimbal with 20 W of output power. The total amount of
mission data is estimated to be 17.9 GB d⁻¹. This means that approximately 4.5 h are needed
for the downlink of the mission data every day.

The power system and data-handling system of *LiteBIRD* use the heritage of past JAXA science missions, such as ASTRO-H, as much as possible. Thus we adopt Space Wire for the on-board data-handling system. This makes the interface checks of the electronic components easier. We adopt a 50 V unregulated bus for the power system. Because of the scan strategy, the solar array panels (SAPs) receive solar radiation at an incident angle of 45°. This may reduce the efficiency of the SAPs by 1/√2, but we selected fixed panels to make the system simple. We choose the SAPs to be close to disk-shaped to avoid diffraction of microwaves from the Sun interfering with the telescopes.

3.7. *Operation concepts*

3.7.1. *Basic principles of operation.* Because *LiteBIRD* needs to observe the whole sky as much as possible, we adopt the following principles of operation: (1) *LiteBIRD* does not make real-time observations or target-of-opportunity (TOO) observations, but continuously makes an all-sky survey; (2) mission data will be downlinked to the primary tracking station, GREAT, once a day for a duration of about 4.5 h; (3) observations may be interrupted during the unloading of the MWs and orbit-keeping maneuvers; and (4) precession of the spacecraft may be stopped and observations may be interrupted in the case of an emergency in the SVM, such as a hardware failure.

In what follows, we describe the outline of mission operation for each operations phase.

3.7.2. *Outline of operation.* *LiteBIRD* will be launched from the Tanegashima Space Center with the H3 rocket. It will be directly inserted into an orbit that approaches the L2 point. Soon after separation from the rocket, the spacecraft establishes three-axis controlled attitude and deploys solar panels to obtain enough power. Then, the spacecraft starts to spin, but not to precess, in order to achieve uniform temperature distribution around the spin axis, which is followed by an initial checkout of the SVM. This initial operations phase and checkout will take approximately a week.

After the initial checkout of the SVM, we will start the health check of the PLM. The launch-
locks of the PMUs are released after the health check. The half-wave plate will be supported by
the holding mechanism. We then start cooling the telescopes with a combination of radiative
cooling and the shield cooler. The Joule–Thomson (JT) coolers and the adiabatic demagneti-
zation refrigerators (ADRs) are turned on at the appropriate timing. This initial cooling takes
a relatively long time, approximately 70 or 80 d. When the nominal operation temperature of
the focal-plane detectors is reached, their function and performance are checked. Thus most
of the cruising phase out to L2, which may last approximately 100 d, will be spent on initial cooling.

When the spacecraft arrives at L2, an insertion maneuver into the Lissajous orbit will be car-
ried out. Then, test observations are conducted in the all-sky scanning mode, i.e., combination
of precession and spin. Various functions and the performance of the mission instruments are
verified, and operational parameters are optimized.

When the test observations are completed, regular observations begin and continue for three
years. In this phase, all-sky survey observations are conducted steadily and we obtain as much
data as possible. Our scan strategy is described in Sect. 5.1. As for calibration of the instru-
ments, our baseline plan is to rely on data from the regular observations, not to pause them
for special calibration data taking. Our in-flight calibration plan is discussed in more detail in
Sect. 4.8. After these regular observations, we may extend the mission, if approved by the Japan
Aerospace Exploration Agency (JAXA) review.

3.8. *Data processing and analyses*

CMB missions typically scan the sky continuously with many detectors at multiple frequencies, measuring temperature and linear polarization, while simultaneously recording the orientation of the telescope. The time-ordered data (TOD) then consist of the time stamp, observation direction determined by satellite attitude monitor, HWP position, thermal and electric monitor for the instruments, and the measured signal for each detector sample. The measured signal includes not just the CMB, but also emission from astrophysical foregrounds, together with other systematic effects, as well as instrumental noise.

The processing of CMB experimental data can be described as a series of steps that move
from the TOD to sky maps at each frequency, which are then separated into different physical
components. The statistics of the CMB map are finally compared to the cosmological pre-
diction from theoretical models. These data-processing steps, indicated in Fig. 7, reduce the
statistical and systematic uncertainties in the data, first reducing the systematic contamination
by appropriate mitigation in a given data domain, and then reducing the dimensionality of the
data set by exploiting its redundancies to project onto a lower-dimensional domain.

Systematic mitigations include removing glitches (e.g., from cosmic-ray hits) in the time do-
main, separating the CMB from the astrophysical foreground components in the map do-
main, and quantifying contamination from unresolved emission sources in the spectral domain.
Throughout the analysis process we also have to account for non-idealities in the instrument,
both optical (e.g., from asymmetric and mismatched beams, including sidelobes, differences in
the bandpass for each detector) and electronic (e.g., gain drift, non-linearity, and crosstalk).

Finally, we need an accurate description of the uncertainties in the products and their correla-
tions. The data volumes that we need to amass in order to detect the tiny CMB signals preclude
exact analyses, and so we typically use Monte Carlo methods for debiasing and forward prop-
agation of uncertainties. We therefore need to be able to generate and reduce large numbers of
very accurate simulated data sets, whose input mission and sky models are themselves informed
by our analyses of the satellite data.

With 4508 detectors sampling at 19.1 Hz for three years, the *LiteBIRD* mission will gather 8 × 10¹² detector samples. Manipulating this data volume while capturing all of the correlations in the CMB signals, foregrounds, and instrumental noise and systematics, with sufficient precision to yield reliable, unbiased results, is a computationally challenging task, requiring the use of
<figure><img src="image_8.png" /><figcaption>**Fig. 7.** Flowchart indicating the sequence of steps leading to the determination of cosmological parameters from mission TOD via several intermediate products that can also be scientifically exploited. Note the iterative nature of the processing.</figcaption></figure>

state-of-the-art high-performance computing systems. Similarly, tracking the provenance of all of the data products, including the myriad data cuts used to check the robustness of the analysis, requires dedicated databases accessible to all collaboration members. The biggest data challenges for *LiteBIRD* will be removing astrophysical foreground contamination using the sky maps at the 15 observing frequency bands (Sect. 5.2), and mitigating systematic effects and precise characterization of their residuals (Sect. 5.3).
<table><caption>**Table 3.** LiteBIRD sensitivities. We show the values related to the sensitivity in 15 frequency bands. From left to right the columns are: the telescope covering the band; the band identification number; the band center frequency in GHz; the bandwidth in GHz and its ratio; the main beam FWHM in arcmin; the detector pixel size in mm; the number of bolometers used; the NET value of a single detector in µK √s; and the NET value of the detector array in µK √s.</caption><thead><tr><th>Tel.</th><th>ID</th><th>ν [GHz]</th><th>δν (δν/ν) [GHz]</th><th>Beam size [arcmin]</th><th>Det. pixel size [mm]</th><th>No. of bolo</th><th>NET detector [µK √s]</th><th>NET array [µK √s]</th></tr></thead><tbody><tr><td>LFT</td><td>1</td><td>40</td><td>12 (0.30)</td><td>70.5</td><td>32</td><td>48</td><td>114.63</td><td>18.50</td></tr><tr><td>LFT</td><td>2</td><td>50</td><td>15 (0.30)</td><td>58.5</td><td>32</td><td>24</td><td>72.48</td><td>16.54</td></tr><tr><td>LFT</td><td>3</td><td>60</td><td>14 (0.23)</td><td>51.1</td><td>32</td><td>48</td><td>65.28</td><td>10.54</td></tr><tr><td rowspan="2">LFT</td><td rowspan="2">4</td><td rowspan="2">68</td><td>16 (0.23)</td><td>41.6</td><td>16</td><td>144</td><td>105.64</td><td>9.84</td></tr><tr><td>16 (0.23)</td><td>47.1</td><td>32</td><td>24</td><td>68.81</td><td>15.70</td></tr><tr><td rowspan="2">LFT</td><td rowspan="2">5</td><td rowspan="2">78</td><td rowspan="2">18 (0.23)</td><td>36.9</td><td>16</td><td>144</td><td>82.51</td><td>8.34 (comb.)</td></tr><tr><td>43.8</td><td>32</td><td>48</td><td>58.61</td><td>7.69</td></tr><tr><td rowspan="2">LFT</td><td rowspan="2">6</td><td rowspan="2">89</td><td rowspan="2">20 (0.23)</td><td>33.0</td><td>16</td><td>144</td><td>65.18</td><td>5.97 (comb.)</td></tr><tr><td>41.5</td><td>32</td><td>24</td><td>62.33</td><td>6.07</td></tr><tr><td rowspan="2">LFT<br>MFT</td><td rowspan="2">7</td><td rowspan="2">100</td><td rowspan="2">23 (0.23)</td><td>30.2</td><td>16</td><td>144</td><td>54.88</td><td>5.11</td></tr><tr><td>37.8</td><td>11.6</td><td>366</td><td>71.70</td><td>4.19</td></tr><tr><td rowspan="2">LFT<br>MFT</td><td rowspan="2">8</td><td rowspan="2">119</td><td rowspan="2">36 (0.30)</td><td>26.3</td><td>16</td><td>144</td><td>40.78</td><td>3.80</td></tr><tr><td>33.6</td><td>11.6</td><td>488</td><td>55.65</td><td>2.82</td></tr><tr><td rowspan="2">LFT<br>MFT</td><td rowspan="2">9</td><td rowspan="2">140</td><td rowspan="2">42 (0.30)</td><td>23.7</td><td>16</td><td>144</td><td>38.44</td><td>2.26 (comb.)</td></tr><tr><td>30.8</td><td>11.6</td><td>366</td><td>54.00</td><td>3.58</td></tr><tr><td rowspan="2">MFT</td><td rowspan="2">10</td><td rowspan="2">166</td><td rowspan="2">50 (0.30)</td><td>28.9</td><td>11.6</td><td>488</td><td>54.37</td><td>2.75</td></tr><tr><td>28.0</td><td>11.6</td><td>366</td><td>59.61</td><td>3.48</td></tr><tr><td>HFT</td><td>11</td><td>195</td><td>59 (0.30)</td><td>28.6</td><td>6.6</td><td>254</td><td>73.96</td><td>5.19</td></tr><tr><td>HFT</td><td>12</td><td>235</td><td>71 (0.30)</td><td>24.7</td><td>6.6</td><td>254</td><td>76.06</td><td>5.34</td></tr><tr><td>HFT</td><td>13</td><td>280</td><td>84 (0.30)</td><td>22.5</td><td>6.6</td><td>254</td><td>97.26</td><td>6.82</td></tr><tr><td>HFT</td><td>14</td><td>337</td><td>101 (0.30)</td><td>20.9</td><td>6.6</td><td>254</td><td>154.64</td><td>10.85</td></tr><tr><td>HFT</td><td>15</td><td>402</td><td>92 (0.23)</td><td>17.9</td><td>5.7</td><td>338</td><td>385.69</td><td>23.45</td></tr><tr><td>Tot.</td><td></td><td></td><td></td><td></td><td></td><td>4508</td><td></td><td></td></tr></tbody></table>

# 4. Payload module of LiteBIRD

## 4.1. Overview

The LiteBIRD PLM consists of three telescopes—at low, medium, and high frequencies—with their respective cryostructure and focal planes cooled down to 0.1 K. The PLM also includes the global cooling chain from 300 K to 4.8 K, and room-temperature elements, such as drivers and warm readout electronics of the detectors. Requirements for the PLM have been derived from the top-level requirement of achieving a tensor-to-scalar ratio error of $\delta r < 0.001$ (see Sect. 3.2). Table 3 gives information on the frequency bands, beam sizes, and noise-equivalent temperatures (NETs) for each of the 15 frequency channels. A discussion of the NET calculations is given in Sect. 5.1.

The LiteBIRD requirements imply technical challenges for the PLM, in terms of sensitivity, optical properties, stability, or even compactness, over a wide range of frequencies, from 34 to
448 GHz. In order to achieve such a challenging set of scientific requirements, an important feature of *LiteBIRD* is its observing strategy, focusing on the largest scales over the sky to maximize the signal expected from the reionization and recombination peaks of the *B*-mode power spectrum, which requires an unprecedented sensitivity over multipoles $2 \le l \le 200$. This demands only reasonably low resolution for the telescopes (<80 arcmin), but associated with a strong control of the systematics in order to minimize the 1/f noise.

In this context, a critical technical choice made for *LiteBIRD* was to use as the first optical element a continuously rotating half-wave plate (HWP). This allows us to distinguish between the instrumental polarized signal and the sky signal, which is modulated at $4f_{HWP}$. While, without the HWP, data from a pair of detectors mutually orthogonal in their polarization orientations are usually combined, causing leakage from temperature to polarization if there are any differences in the beams, gains, or bandpasses between the two detectors, this can be removed through the use of HWPs that enable us to measure the polarization using a single detector. Lastly, the presence of the continuously rotating HWP performs an effective suppression of the 1/f noise. A detailed trade-off analysis, including the polarization effects induced by the HWP itself, has been carried out between the two cases, i.e., with and without the HWP, demonstrating that the performance without HWP is expected to have potential large systematic effects compared with that with HWP, as described in Sect. 5.3.1. Hence, in order to guarantee appropriate thermal performance in terms of stability and minimal heat load, the three telescopes will be equipped with polarization modulator units (PMUs) continuously rotating at a few Hz around a stable temperature below 20 K, using a magnetic levitating mechanism with superconducting bearing, as described in more detail in Sects. 4.2.4 and 4.3.3.

The distribution and the number of bands over a wide range of frequencies, from 34 GHz to 448 GHz, have been optimized to deal with the following constraints: the spectral resolution has to ensure the appropriate characterization of the expected complexity of the spectral energy distribution of the synchrotron and dust Galactic foregrounds, leading to 15 broad and partially overlapping bands; the limited frequency range of HWP materials (sapphire and metal mesh) and associated anti-reflection coating required us to split into three telescopes; the spectral mapping of the CO lines has to be optimized by rejecting such molecular lines from some of the bands and including them in others (notice that notch filters have not been included, since it has been demonstrated that temperature-to-polarization leakage from CO lines is highly reduced by the rotating HWP); and finally an overlap between bands and instruments had to be foreseen to mitigate systematic effects. We ended up with the following distribution: a reflective telescope at low frequency (see Sect. 4.2), the LFT (34–161 GHz), and two refractive telescopes at middle and high frequencies (see Sect. 4.3), the MFT (89–225 GHz) and HFT (166–448 GHz), as illustrated in Fig. 8. The MFT and HFT telescopes are mounted on the same mechanical structure, and point in the opposite direction compared to the LFT, but cover the same circle over the sky when spinning.

The focal planes of the three telescopes with large fields of view ($18^\circ \times 9^\circ$ for LFT, and $28^\circ$ diameter for MFT and HFT) are populated with multichroic polarized transition-edge sensor (TES) detectors (one to three bands per pixel). This multichroic technology allows for a very compact design with sufficient flexibility on the optimization of the sensitivity per band that is needed to improve the performance of the component-separation techniques. Two detector technologies have been used, lenslet-coupled detectors for the LFT and MFT, and horn-coupled detectors for the HFT, for a total of 4508 detectors cooled down to 100 mK, as detailed
<figure><img src="image_9.png" /><figcaption>**Fig. 8.** Payload module overview showing the surrounding V-grooves acting as passive coolers up to 30 K, with the 4.8-K enclosure of the low-frequency crossed-Dragone telescope in the front, and the two 4.8-K tubes of the mid- and high-frequency on-axis telescopes in the back.</figcaption></figure>

in Sect. 4.4. The readout electronics takes advantage of the frequency multiplexing scheme to
accommodate this large set of detectors without loss of information and minimal power dissi-
pation on the focal planes.

The temperature stability of the instruments is another crucial point for CMB *B*-mode polar-
ization probes because of the following aspects: the temperature fluctuation of the optical com-
ponents contributes to noise stability and 1/f noise; and temperature variation of the mechani-
cal structures has a direct impact on pointing stability. Hence the three *LiteBIRD* telescopes are
fully cooled down to 4.8 K, minimizing the heat load on the focal planes. The proposed 300-K
to 4.8-K cryogenic chain for *LiteBIRD* is based on the architecture developed as part of the
*SPICA*-SAFARI mission. It combines radiative cooling (V-grooves) down to 30 K combined
with mechanical cryo-coolers to provide cooling to temperatures down to about 4.8 K. In its
current definition, a 15-K pulse-tube cooler associated with three V-groove radiators, respec-
tively at 160 K, 90 K, and 30 K, intercepts part of the thermal loads. Then, one helium JT loop
(4-K JT, <sup>4</sup>He), pre-cooled by two 2-stage Stirling coolers (100 K/20 K). All telescopes have in-
termediate cold stages at 1.75 K and 0.35 K between their mechanical enclosure at 4.8 K and
the detectors at 0.1 K. The 1.75-K cooler is based on a 2-K Joule–Thomson cooler, to provide a
continuous cooling at 1.75 K. The sub-kelvin cooler is made of two ADR stages in series to pro-
vide stable and continuous cooling at 0.35 K, combined with two other ADR stages in parallel
for the 0.1-K stage. Again, the design of this cryochain has been optimized to ensure maximum
stability of the temperature of the focal planes and the optical elements of the telescopes.

In the following sections, we provide more details on the instrumental setup, following the
natural path of the scientific signal, i.e., starting with the optical and mechanical descriptions
of the LFT (Sect. 4.2) and MFT and HFT (Sect. 4.3) telescopes. Since the detection chain of
the three telescopes follows a common architecture, it is globally described in Sect. 4.4 for LFT,
MFT, and HFT, while the global electrical architecture of the PLM is detailed in Sect. 4.6. A
description of the whole cooling chain from 300 K down to 100 mK is provided in Sect. 4.7.
<figure><img src="image_10.png" /><figcaption>**Fig. 9.** Overview of the low-frequency telescope (LFT). The mid- and high-frequency telescopes and side panels are not shown for clarity.</figcaption></figure>

Finally, the ground and in-flight calibration plan of the whole instrumental setup is discussed in Sect. 4.8.

## 4.2. *Low-frequency telescope*

4.2.1. *Overview.* With an aperture diameter of 400 mm and an angular resolution ranging from 24 to 71 arcmin, LFT consists of nine broad frequency bands spanning 34 to 161 GHz, in order to cover the spectral domains of both CMB and synchrotron radiation emission. It is operated at a cryogenic temperature of 4.8 K to reduce the optical loading, and surrounded by radiators called V-grooves, acting as passive coolers. The LFT optical design follows a crossed-Dragone configuration, with an antenna made of aluminum. As the first optical component, a polarization modulator unit (PMU), consisting of a continuously rotating transmissive half-wave plate, is mounted in front of an aperture stop, allowing us to minimize straylight contamination. The LFT focal plane is based on multichroic TES detectors cooled down to 100 mK, as described in Sect. 4.4.1. A frame structure at 5 K supports all components: the PMU; focal plane; primary and secondary reflectors; and absorbers. An overview of the LFT is presented in Fig. 9, introducing the various components listed above.

Performance requirements of the LFT are described in Ref. [178] and a design flow is shown in Fig. 10. Starting from an optical design satisfying the instrument requirements, we proceeded with physical optics simulations and by completing the structural design to correctly match the interface requirements. A scaled version of LFT has allowed us to validate the models based on the scaled model measurements [174].

4.2.2. *Optical design.* The challenges of LiteBIRD include its wide field of view (FoV) and broadband capabilities for millimeter-wave polarization measurements, which are derived from the sensitivity requirements. The wide FoV corresponds to a large focal-plane area, so that a detector pixel has different spill-over or edge-taper at reflectors depending on the pixel position on the focal plane. Possible paths of straylight increase with a wider FoV. After various trade-off studies of various optical configurations, including a front-fed Dragone [179], we concluded
<figure><img src="image_11.png" /><figcaption>**Fig. 10.** Design flow of LFT. From the instrument requirements, the optical design, physical optics simulations, structural design, interface requirements, a scaled version of LFT, and verification plan are designed and developed either sequentially or in parallel.</figcaption></figure>

<table><caption>**Table 4.** Optical specifications of LFT [178]. The point spread function (PSF) flattening is defined as $(\sigma_{maj} - \sigma_{min})/(\sigma_{maj} + \sigma_{min})$ where $\sigma_{maj}$ and $\sigma_{min}$ are for the major and minor axes, respectively.</caption><tr><td>Aperture diameter</td><td>400 mm</td></tr><tr><td>Field of view</td><td>18° × 9°</td></tr><tr><td>Strehl ratio</td><td>&gt;0.95 at 161 GHz</td></tr><tr><td>Focal-plane telecentricity</td><td>&lt;1.0°</td></tr><tr><td>F-number, f/N</td><td>2.9 &lt; N &lt; 3.1</td></tr><tr><td>PSF flattening</td><td>&lt;5%</td></tr><tr><td>Cross-polarization</td><td>&lt;−30 dB</td></tr><tr><td>Rotation of polarization angle across FoV</td><td>&lt;±1.5°</td></tr></table>

that the crossed-Dragone antenna is the best option for LFT, because it has good beam and polarization performance over the required FoV.

The crossed-Dragone antenna of LFT has been designed with anamorphic aspherical surfaces [180] to achieve the specifications listed in Table 4. A ray diagram of LFT is shown in Fig. 11, which has an FoV of 18° × 9°. The f/3.0 ratio and crossing angle of 90° between the aperture to primary and the secondary to focus axes have been chosen after an extensive straylight study. While the requirement on far-sidelobe knowledge (about −56 dB) is one of the most challenging requirements, the optical design has been optimized to achieve far-sidelobe levels as low as possible, ideally below the knowledge requirement threshold, in order to be able to mitigate the need of far-sidelobe high-accuracy measurements. Indeed, the expected beam-calibration sequence plans to go through room-temperature measurements of far sidelobes, cryogenic measurements of near sidelobes, and in-flight calibration of near sidelobes, where we define the near sidelobes to be the region out to 3° with respect to the main-lobe peak direction, and the remaining part of the beam is defined as the far sidelobes.
<figure><img src="image_12.png" /><figcaption>**Fig. 11.** Ray-tracing diagram of LFT.</figcaption></figure>

#### 4.2.2.1 Optical components

An aperture stop at 4.8 K, with an inner diameter of 400 mm, is made of millimeter absorber, TK-RAM [181,182] on an aluminum plate. This works to create the desired beam shape and to reduce the photon noise for the configuration with an edge-taper of about 3 dB. Primary and secondary reflectors made of aluminum (A6061) have a rectangular shape of 835 mm × 795 mm and 872 mm × 739 mm, respectively, with serrations to reduce diffraction patterns from the edges of mirrors.

Millimeter absorbers (to reduce reflections) are attached on the inside surface of the 5-K frame, which plays the role of a cavity. TK-RAM, Simons Observatory metamaterial microwave absorber [183], and 3D-printed absorber [184] are candidates for such an absorber as described in Sect. 4.3.3. Eccosorb AN72 and HR10 are also candidates; however, they have large total mass loss (TML) and collected volatile condensable material (CVCM). According to the NASA outgas database [185], AN72 washed with ethanol shows reasonable TML and CVCM values. A front hood whose height is 500 mm reduces straylight to the far sidelobes. The aperture shape of the front hood is described in Ref. [174].

#### 4.2.2.2 Optical simulations

Physical optics simulations of LFT with GRASP10 [186] are reported in Ref. [187], with the simulated telescope elements including LFT reflectors and the aperture stop. The feed pattern is assumed to be a Gaussian beam, but the real feed pattern may change the antenna pattern on the sky. At this stage, the HWP, which may generate additional sidelobes, is not taken into account for the physical optics simulations.

#### 4.2.2.3 Structural design

The frame and reflectors of LFT are made of aluminum (A6061) in order to shrink similarly by 0.4% to 4.8 K from 300 K. The telescope is covered with aluminum and absorbers to reduce straylight from the inner surface of the V-groove. The mass of LFT, including the focal plane, is estimated to be approximately 200 kg. The telescope is supported by trusses made of aluminum on the 4.8-K interface plate, as illustrated in Fig. 12.

### 4.2.3. Scaled model demonstration.
A quarter (1/4)-size scaled model of LFT (see Fig. 13) has been designed and developed to characterize the antenna pattern in the near field [174]. The observed frequencies are also scaled, so that the antenna pattern of the scaled model matches that of the full-size one. The measured antenna patterns are then transformed to far fields,
<figure><img src="image_13.png" /><figcaption>Fig. 12. LFT structure.</figcaption></figure>

<figure><img src="image_14.png" /></figure>

<figure><img src="image_15.png" /><figcaption>**Fig. 13.** Left: LFT quarter (1/4) scaled model and its near-field measurement system. Right: Far-field patterns of the quarter LFT at the center (Pos. A), the left upper edge (Pos. B), and the left bottom edge (Pos C) of the focal plane measured at 220 GHz (which corresponds to 55 GHz for the full-scale LFT [174]).</figcaption></figure>

as shown in Fig. 13. Based on these scaled model measurements, we confirmed the wide-field performance of LFT and the suppression of far sidelobes.

#### 4.2.4. *LFT polarization modulation unit.*
The baseline configuration of the *LiteBIRD* LFT PMU consists of a Pancharatnam-type multilayer sapphire stack as an achromatic half-wave plate (AHWP), which is supported by a cryogenically cooled rotational mechanism. A similar system was employed by a balloon-borne CMB experiment, E and B EXperiment (EBEX), and has been under development by multiple ground-based experiments, e.g., POLARBEAR-2 and Simons Observatory [188–190]. Here we describe a summary of the current development status using the PMU breadboard model (BBM) during the conceptual design phase. This BBM is aimed at demonstrating some of the key technological challenges, as we will highlight later. Figure 14 shows the overview and components of the current PMU BBM; a more detailed overview can be found in Ref. [191].
<figure><img src="image_16.png" /><figcaption>**Fig. 14.** Overview and components of the LiteBIRD LFT PMU BBM. The AHWP is composed of five-layer sapphire plates that are about 500 mm in diameter with moth-eye sub-wavelength grating structures for anti-reflection on two outer surfaces. The entire AHWP is held in a leaf-like holder, which accounts for the differential thermal contact and yet is strong enough to survive the launch impact and vibration. The rotational mechanism is composed of the cryogenic holder mechanism (called the “gripper”), the optical encoder for monitoring the rotor position, and the drive motor mechanism to drive the rotor. The rotation is supported by the superconducting bearing, ring magnet, and ring YBCO. The entire rotor is held by the launch lock in order to survive the launch impact.</figcaption></figure>

The AHWP is continuously rotated by the cryogenic rotation mechanism that consists of the superconducting magnetic bearing (SMB) and the synchronous motor spinning at a rotation speed of 46 rpm throughout the mission. The AHWP covers the observational frequency band of LFT. The broadband anti-reflection coating is achieved using sub-wavelength structures directly machined by a laser. The small diameter sample demonstration achieved the measured transmittance of 91% and 97% for the 40- and 50-GHz LFT bands, respectively, and above 98% for other frequency bands [192]. Most recently, we made a sample with a diameter up to 80 mm [193]. The current machining strategy is scalable in diameter, and a demonstration with larger diameter samples (200 mm and 330 mm) is in progress. The high modulation efficiency is realized using multilayered sapphire plates based on a Pancharatnam recipe. We plan to employ five-layer sapphire plates, which achieve an averaged modulation efficiency of about 92% and 96% for the 40- and 140-GHz LFT bands, respectively, and above 98% for other frequency bands, as well as nulling the frequency-dependent fast-axis variation over the LFT bandwidth [194–196]. The multilayer sapphires will be glued by using a sodium silicate solution. The first preliminary tests with a polished 4 mm × 4 mm surface show that the mechanical strength is >20 MPa, which is sufficiently high to mechanically treat the multilayer sapphire stack as one bulk sample under the launch impact [197]. We also tested whether there is any effect on the millimeter-wave transmittance with this bonding scheme using a sapphire sample with a diameter of 100 mm, and we did not find any effect within the noise level of the measurement, equal to 2% of the signal. We are continuing to address this evaluation with a
larger diameter sample and high-accuracy millimeter-wave characterization. The AHWP is the first optical element of the LFT and it is held to the telescope structure using both the launch lock system and the cryogenic holder mechanism. The launch lock will be released soon after launch. The cryogenic holder mechanism is used to maintain the rotor in place during launch and cool-down, before the rotor thermalizes and levitates thanks to the high-temperature superconductor bulks. It also functions as a heat path that thermalizes the rotor to the operating temperature of 4.8 K. The combination of the SMB and the synchronous motor achieves fully contact-free rotation to minimize the heat dissipation from physical contact, as well as giving no wear-and-tear during the mission. The required AHWP temperature during science operations has to be less than 20 K in order to reduce thermal emission from the AHWP itself. The corresponding maximum heat dissipation that the rotor can accept is < 1 mW. Despite having no physical contact, a source of heat dissipation can still come from magnetic friction. The key development items are to achieve a uniform magnetic field of the rotor magnet, along with lightweight mechanical and thermal design, without using metal to minimize the eddy currents. The status of this development is detailed in Ref. [198].

The absolute and relative angular positions of the AHWP with respect to the instrument frame are monitored by using a cryogenically compatible optical encoder, which consists of an LED and a photodiode. We developed an angular encoder readout system, which consists of an optical chopper between the LED and photodiode. The encoder from the photodiode is read using a field-programmable gate array (FPGA) with an analog-to-digital converter (ADC) and we have demonstrated reconstruction of the position angle to better than 1 arcmin with the dedicated algorithm. This analysis, together with identifying the source of the position angle uncertainties, is reported in Ref. [199]. The absolute polarization angle referenced to sky coordinates will be calibrated by some other means, e.g., nulling $C_{\ell}^{EB}$ or using polarized astrophysical sources (see Sect. 4.8).

Mitigation of systematic effects for low-$\ell$ reconstruction makes the PMU the key to the success of the mission. Current efforts shall lead the design of the demonstration and engineering models by working with companies that are qualified to procure the flight hardware.

### 4.3. Mid- and high-frequency telescopes

4.3.1. *Overview.* The optimization of the instrumental design over the mid- and high-frequency ranges of LiteBIRD, spanning from 89 to 448 GHz, led to a design with two fully refractive telescopes, as shown in Fig. 15. The frequency bands of the MFT range from 89 to 224 GHz, and from 166 to 448 GHz for the HFT (see Ref. [200] for more details). When considered together, the two telescopes are referred to as the mid- and high-frequency telescopes (MHFT).

The choice to use two distinct fully refractive telescopes was mainly driven by the constraints put on the HWP material and the anti-reflection coatings (ARCs), imposed by the broad frequency coverage and the limited mass budget and volume allocation. Each telescope features its own polarization modulator, in order to mitigate the bandwidth limitations of the HWP mesh technology. The global design specifications of the MFT and HFT are summarized in Table 5. This design benefits from the broad expertise gained on many current and upcoming sub-orbital CMB experiments, such as BICEP/Keck [201], SPIDER [202], LSPE [203], and Simons Observatory [204]. With these very compact on-axis designs, the MFT and HFT match the volume and weight constraints, mitigate straylight issues, and split the entire frequency range into two
<figure><img src="image_17.png" /><figcaption>Fig. 15. Overview of the mid- and high-frequency telescopes.</figcaption></figure>

<table><caption>**Table 5.** Global design specifications of MFT and HFT.</caption><thead><tr><th></th><th>MFT</th><th>HFT</th></tr></thead><tbody><tr><td>Frequency coverage</td><td>89–224 GHz<br>5 observation bands</td><td>166–448 GHz<br>5 observation bands</td></tr><tr><td>Number of detectors</td><td>2074</td><td>1354</td></tr><tr><td>Aperture diameter</td><td>300 mm</td><td>200 mm</td></tr><tr><td>Rotational HWP speed</td><td>39 rpm</td><td>61 rpm</td></tr><tr><td>Field of view</td><td colspan="2">Ø28°</td></tr><tr><td>Angular resolution</td><td colspan="2">&lt; 30 arcmin</td></tr><tr><td>Volume allocation at 5 K</td><td colspan="2">1700 mm × 1400 mm × 750 mm</td></tr><tr><td>Mass budget at 5 K</td><td colspan="2">100 kg</td></tr></tbody></table>

bands. This choice also offers more flexibility for an optimal design of the separate filtering chains. Dealing with two smaller compact telescopes will considerably simplify the assembly, integration, and testing (AIT) and assembly, integration, and verification (AIV) phases of the project and the ground-calibration activities. On the other hand, careful design and modeling are needed for the polypropylene (PP) lenses and transmissive metamaterials; see Sect. 4.3.2. Finally, MFT and HFT assemblies are held on a single mechanical structure cooled down to 4.8 K, which contains the sub-4.8 K parts of the cryochain.

### 4.3.2. *Optical design.*
The optical configurations of MFT and HFT are shown in Fig. 16. Both telescopes have f/2.2, with an aperture stop (300 mm and 200 mm in diameter, for MFT and HFT, respectively) located skywards of the two lenses. The stop also serves as a convenient location for the transmissive HWP, which is located very close to (but slightly sky-side of) the stop.

Both systems are diffraction-limited to the upper edge of their respective bands, across a 28° diameter field of view, and have telecentric focal planes. Initial physical optics simulations for
<figure><img src="image_18.png" /><figcaption>**Fig. 16.** Ray-tracing diagrams for MFT (left) and HFT (right). The on-axis and off-axis fields (14°) are the blue and red rays, respectively. The telescope aperture is located at $z = 0$, with a diameter of 300 mm and 200 mm for MFT and HFT, respectively. The lens material is polypropylene.</figcaption></figure>

the MFT also indicate uniform beam shapes, with low cross-polarization and ellipticity smaller than 0.03, across the field of view. The HFT optical performance is very similar. A more detailed review of the performance analysis of the MFT and the HFT systems is discussed in Ref. [205].

An axisymmetrical optical design for the MFT and HFT has been adopted to remain simple with excellent performance, while being relatively relaxed in terms of optical tolerances. However, this creates optical modeling challenges due to refractive surfaces and metamaterials. Some performance validation is needed to address both the issues related to intrinsic frequency-, polarization-, and temperature-dependent properties of the refracting materials. It will be essential to understand the higher-order optical coupling effects arising from a broad set of non-idealities, like imperfect dielectric-to-vacuum matching at the optical interfaces, imperfectly absorbing tube surfaces and focal planes, scattering off internal surfaces, and thermal radiation pickup from the payload environment.

### 4.3.2.1 Half-wave plate

While the electromagnetic behavior of the mesh HWP is very well modeled and validated at the subsystem level, the presence of a mesh HWP along the optical path to the focal plane makes it necessary to model the whole system with accuracies beyond what is achievable with currently available simulation software. The need to capture the impact of imperfect and frequency-dependent phase shifts and the effect of non-normal incidence on the final performance of the device creates an extremely complex modeling effort. The HWP imperfections might modulate the background and lead to a strong synchronous signal peaked at harmonics of the HWP rotation frequency. Such an HWP synchronous signal (HWPSS) has been observed using Maxima [206], EBEX [207], POLARBEAR [208], and NIKA [209], each of which used a continuously rotating HWP, similarly to the *LiteBIRD* case. The parasitic HWPSS can be modeled and subtracted in the data analysis process [209]. However any residual could act as an additional noise in the polarization data and increase the total error budget. In order to reach the required accuracy it will be crucial to characterize and model this at the system level as a result of beam propagation through the whole optical chain, including the HWP, quasi-optical filters, optical elements, and focal-plane beam formers. This effort is in progress.

### 4.3.2.2 Optical ghosts

Ghosts are detectable effects arising from a variety of non-idealities in the optical system, mostly due to multiple internal reflections that partially re-focus the light away from the intended location on the focal plane. Image and polarization artifacts due to this effect must be clearly identified, modeled, and compared with the actual behavior of the optical system. A systematic study on these effects needs to be carried out to evaluate their impact on the final
<figure><img src="image_19.png" /><figcaption>**Fig. 17.** Left: Example of optical ghosting at 90 GHz, from the combined effect of a non-ideal ARC (in this case a single-layer ARC optimized for 150 GHz) on MFT lenses and imperfect absorption on the focal plane, as seen in the telescope far field. A secondary beam-like feature can be seen out of the main beam pattern in this example. Right: Corresponding power distribution in the plane of the telescope, as predicted by these simulations.</figcaption></figure>

performance of the MHFT instruments. As reported in Ref. [205], a preliminary study was performed at 90 GHz on the MFT to characterize multiple reflections off optical surfaces. This analysis showed a diffuse contamination from ghosting across the focal plane at the level of -40 dB of the peak level of the nominal focused image, with resulting artifacts in the reconstructed image at scales of a few degrees on the sky (see Fig. 17).

### 4.3.3. *Subsystems.*
We detail below the various subsystems of the two telescopes, starting from the first optical component encountered, the rotating HWP, down to the mechanical structure.

#### 4.3.3.1 PMU design and development

The polarization modulator units (PMUs) for the MFT and HFT are based on spinning HWPs. The mesh-filter technology [210] provides ultra-light transmissive HWPs and has been adopted for both telescopes. While this technology offers a large gain in mass compared to sapphire HWPs, the current mesh-HWP bandwidth would not cover the whole LFT bandwidth, whereas it can more easily accommodate the MFT and HFT bandwidths. Moreover, facilities already in place allow us to manufacture large diameter devices (up to 60 cm diameter). The mesh HWPs consist of polypropylene-embedded anisotropic metal grids, AR-coated on both sides (see Fig. 18). These devices emulate the behavior of birefringent materials by means of orthogonally oriented stacks of capacitive and inductive grids [211,212]. The expected transmission coefficients and the polarization modulation efficiencies across the MHFT bands are, respectively, approximately 95% and greater than 95%, for MFT and HFT, respectively. The estimated weights of the HFT and MFT wave plates are approximately 100 g and 400 g, respectively. A detailed description of the mesh-HWP design and manufacture can be found in Ref. [213].

The rotation mechanisms have the same design for both MFT and HFT, and shall meet several stringent requirements, in terms of mass (< 20 kg), dimension (< 200 mm and < 300 mm), stiffness, power dissipation (< 4 mW), HWP temperature (< 20 K [214]), and technology readiness level (TRL), for the levitation, driving, and gripping mechanisms, as well as position encoder.
<figure><img src="image_20.png" /><figcaption>**Fig. 18.** Left: Model showing a small portion of a mesh HWP with embedded stacks of capacitive and inductive grids. Right: Mesh -WP prototype working between 100 and 300 GHz and being around 3 mm thick.</figcaption></figure>

<figure><img src="image_21.png" /><figcaption>**Fig. 19.** Left: Overview of the PMU design. The coil rings are removed to show the encoder on the edge of the rotor. Right: PMU cross-section.</figcaption></figure>

A very low friction superconducting magnetic bearing [215] based on the magnetic levitation between a YBCO superconductor ring (stator) and an SmCo (samarium–cobalt) permanent magnet ring (rotor) hosts the HWPs (Fig. 19).

The rotation is driven by an electromagnetic motor, based on the interaction between eight small cylindrical SmCo magnets placed on the edge of the rotor and 64 high-purity copper coils placed on the stator. The motor magnets and the hysteresis in the main magnet assembly are the main contributions to the power load on the 5-K stage and must be minimized as much as possible. In addition, the eddy currents induced by the motor coils heat up the rotor, which can be cooled down only by radiation, a process that is not very efficient at cryogenic temperatures. The total heat load expected *from both mechanisms* is 2.8 mW, which is within the requirement, with a 40% margin.

The rotor temperature is monitored by capacitive sensors [216] (3% accuracy), which are also used to monitor the levitation height and the wobble of the rotor (10 µm resolution). A thermal model built by Comsol Multiphysics<fnref n="7" /> shows that after a slow rise the equilibrium temperature should be approximately 16 K for both modulators, assuming HWP emissivities of 0.02 and 0.03 for MFT and HFT, respectively, while the assumed emissivity of aluminum is 0.5, achievable with a blackened surface [217].

<footnote n="7">⁷https://www.comsol.com.</footnote>
The position readout system uses an optical encoder, with 64 precision slits in the rotor ring periphery. The light from a warm temperature modulated LED is transferred to the rotor via an optical fiber, and the light transmitted through the slits is transferred back to a warm temperature detector via another optical fiber. This configuration minimizes the heat load on the different stages of the cryogenic system [218]. The expected angular encoding accuracy is better than 0.1 arcmin and can be improved through a Kalman filter using the high rotation stability (< 1 mHz) and the inertia of the system. A simple and reliable clamp/release system [219] (with zero power dissipation while holding the rotor, and zero power dissipation when the rotor is released) has been developed. It is expected to be used only once at the beginning of the flight; nevertheless, the system was designed to be able to clamp and release the rotor as many times as needed.

#### 4.3.3.2 Lens components

The baseline design employs lenses manufactured from polypropylene, and anti-reflection coating with a matching layer of porous polytetrafluoroethane (PTFE). This coated-lens technology has been well characterized and validated through an extensive ESA-funded Technical Research Programme. Lenses of similar sizes have been previously manufactured by members of the project team, and successfully deployed on sub-orbital CMB polarimetry experiments. In addition, porous PTFE-coated lenses have also been deployed in space on the Herschel-SPIRE satellite instrument. As such, the coated lenses demonstrate a high level of technical maturity, operating in a cryogenic vacuum environment. However, over the coming months, we will additionally undertake a significant program of precision characterization of these materials at cryogenic temperature (losses, stress-induced birefringence, etc.).

#### 4.3.3.3 Absorbers

While far-infrared filters will mainly be used to prevent out-of-band radiation from propagating into the telescope, optical absorbers will also be used to prevent or mitigate spurious in-band reflections across the optics tubes. The need for a reliable, light, thermally uniform, space-qualified material has been recognized as a driver for a dedicated study, meant to investigate a set of candidate absorbing materials and/or metamaterial structures. This study will compare traditional absorber candidates such as Thomas-Keating tiles or Eccosorb HR10/AN72 to micromachined, 3D-printed, and injection-molded metamaterials [183,184,220,221]. The study will include detailed laboratory measurements and commensurate electromagnetic simulations of the candidate absorbers spanning the entire MHFT frequency range. The results of this work will allow us to perform a trade-off study to select the best solution for absorbers.

#### 4.3.3.4 Filtering scheme

Although band definition is achieved via on-chip filtering, additional optical filters are required in order to control the out-of-band rejection level, to protect the detectors from straylight, and to control the thermal environment. For MFT we are proposing deployment of a chain of four low-pass filters positioned at the 4.8-K, 2-K, 300-mK, and 100-mK stages. It is noted that the HWP also acts as a low-pass filter and we have the option of adding a high-pass element at the detectors should this be required. The average in-band transmission over the frequency range of the MFT (or HFT) for each of these elements can be targeted to be 95%.
<figure><img src="image_22.png" /><figcaption>**Fig. 20.** Two options of the MHFT mechanical structure design based on a mechanical interface with the satellite at the 4.8-K stage (left) and the 30-K stage (right).</figcaption></figure>

#### 4.3.3.5 Mechanical structure

The mechanical structure is composed of two main parts: the two telescope tubes and an exoskeleton. The telescope tubes are designed to hold the optical elements and the various subsystems, and to ensure optical alignment for each of the two telescopes. The exoskeleton holds the two tubes, connects the telescopes to the payload module, and provides the thermal link to the cryochain. All the mechanical elements are made of material compliant with the optical, mechanical, and thermal constraints, such as aluminum and carbon fiber reinforced plastic (CFRP).

A first series of iterations on the mechanical design has been performed to optimize the mechanical structure, taking into account the various constraints such as minimum eigenfrequencies, total mass, launch load, and thermal conduction (design shown on the left side of Fig. 20). In the initial design, the mass of the MHFT is about 118 kg without margins, which is over the allocated 100 kg value. This specification on the mass is mostly driven by the parasitic heat load on the 4.8-K stage due to the thermal conductance of the satellite mechanical structure holding both LFT and MHFT.

To deal with the stringent constraints on the total mass budget at 4.8 K, we decided to study another option, which consists of moving the mechanical interface with the satellite from the 4.8-K stage to the 30-K stage of the PLM. The total mass budget has been revised in the framework of this second option. The heavy 4.8-K interface ring, shared by LFT and MHFT in the first option design, has now been replaced by two 30-K to 4.8-K optimized cryomechanical structures made of CFRP. We designed the 30-K to 4.8-K cryomechanical structure with particular attention to the thermal conductance. The design of the MHFT tubes is similar to the first option (design shown in the right panel of Fig. 20). This solution allows us to drastically reduce the mass of the 4.8-K interface with the satellite, while minimizing the parasitic heat load on the coldest stages. The study of this mechanical structure design shows that the constraints on the eigen-frequencies and on the parasitic heat load are satisfied.

### 4.4. Detection chain

LiteBIRD will be equipped with 1030 multichroic pixels sensitive to polarization, totaling 4508 TESs, distributed over the three focal planes of LFT, MFT, and HFT. Detector specifications for each of the LiteBIRD bands are shown in Tables 6 and 7. The detection chains of the three telescopes have been designed using a very similar architecture that is described in this
<table><caption>**Table 6.** Summary of the common optical and bolometric design goals of the LiteBIRD detectors. We expect that there will be little deviation from these goals during the development of the focal-plane units (FPUs) for LiteBIRD.</caption><thead><tr><th>Parameter</th><th>Design value</th></tr></thead><tbody><tr><td>TES normal resistance</td><td>1.0</td></tr><tr><td>TES operating resistance</td><td>0.6–0.8 Ω</td></tr><tr><td>Parasitic series resistance</td><td>0.05–0.2 Ω</td></tr><tr><td>FPU (T<sub>b</sub>)</td><td>0.100 K</td></tr><tr><td>Transition temperature (T<sub>c</sub>)</td><td>0.171 K</td></tr><tr><td>Cross wafer T<sub>c</sub> variation</td><td>≤ 7%</td></tr><tr><td>Minimum operating power</td><td>2.5 × optical power</td></tr><tr><td>Pixel in-band optical efficiency</td><td>≥ 70%</td></tr><tr><td>Thermal carrier</td><td>Phonon (n = 3)</td></tr><tr><td>Intrinsic time constant (τ<sub>0</sub>)</td><td>33 ms</td></tr><tr><td>Loopgain during operation</td><td>≥ 10</td></tr><tr><td>Common 1/f knee</td><td>≤ 20 mHz</td></tr><tr><td>FPU lifetime</td><td>≥ 3 yr</td></tr><tr><td>On-sky end-to-end yield</td><td>≥ 80%</td></tr></tbody></table>

<table><caption>**Table 7.** Optical specifications for the LiteBIRD detectors. The values listed in this table flow down from the noise specifications listed in Table 3.</caption><thead><tr><th>Pixel ID</th><th>Frequency [GHz]</th><th>Bolometer count</th><th>Bandwidth Δ<sub>v</sub>/ν</th><th>P<sub>opt</sub> [pW]</th></tr></thead><tbody><tr><td>LF1</td><td>40/60/78</td><td>48</td><td>0.30/0.23/0.23</td><td>0.358/0.300/0.303</td></tr><tr><td>LF2</td><td>50/68/89</td><td>24</td><td>0.30/0.23/0.23</td><td>0.386/0.302/0.311</td></tr><tr><td>LF3</td><td>68/89/119</td><td>144</td><td>0.23/0.23/0.30</td><td>0.367/0.363/0.449</td></tr><tr><td>LF4</td><td>78/100/140</td><td>144</td><td>0.23/0.23/0.30</td><td>0.367/0.356/0.440</td></tr><tr><td>MF1</td><td>100/140/195</td><td>366</td><td>0.23/0.30/0.30</td><td>0.411/0.463/0.386</td></tr><tr><td>MF2</td><td>119/166</td><td>488</td><td>0.30/0.30</td><td>0.496/0.416</td></tr><tr><td>HF1</td><td>195/280</td><td>254</td><td>0.30/0.30</td><td>0.782/0.486</td></tr><tr><td>HF2</td><td>235/337</td><td>254</td><td>0.30/0.30</td><td>0.603/0.384</td></tr><tr><td>HF3</td><td>402</td><td>338</td><td>0.23</td><td>0.290</td></tr></tbody></table>

section for the three telescopes. It includes focal planes and associated readout electronics, both cold and warm parts. More details on the design and fabrication of the detector modules can be found in Ref. [222].

4.4.1. Focal-plane units. LiteBIRD will deploy for each of the telescopes an FPU, which consists of the following components: (i) a focal-plane structure (FPS) providing thermal insulation from the Joule–Thomson 4.8-K cooled stage (4-K JT) and thermal connections to the Joule–Thomson 1.75-K cooled stage (2-K JT) and adiabatic demagnetization refrigerator that cools the sub-kelvin stages (Sub-K ADR), which provide the cooling power to the intermediate temperature stages, cooled down to 1.75 K, 350 mK, and 100 mK; (ii) and a set of individual arrays of detectors, the focal-plane module (FPM), operated at 100 mK. Each FPM consists of a single detector array, optical coupling hardware (lenslet or horn arrays, backshort wafers, etc.), the cryogenic readout units (CRU), and mechanical structures that hold these parts together and provide an interface to the FPS.
<figure><img src="image_23.png" /><figcaption>**Fig. 21.** Low-, mid-, and high-frequency focal-plane units. The LF-FPU rectangular shape is matched to the LFT's oblong FoV using square FPM tiles. The mid- and high-frequency telescopes both have circular FoVs and therefore employ hexagonal arrays arranged in a close-packed pattern. Pixel types are color coded and the details of each can be found in Table 8.</figcaption></figure>

<table><caption>**Table 8.** Focal-plane configurations for the low-frequency focal-plane unit (LF-FPU), mid-frequency focal-plane unit (MF-FPU), and high-frequency focal-plane unit (HF-FPU). The colors in the frequency column correspond to those in Fig. 21.</caption><thead><tr><th>Telescope</th><th>Detector type</th><th>Module</th><th>Frequency [GHz]</th><th>Pixel size [mm]</th><th>Module count</th><th>Pixel count</th><th>Detector count</th></tr></thead><tbody><tr><td rowspan="10">LFT</td><td rowspan="3">LF12</td><td rowspan="3">LF34</td><td>40/60/78</td><td>32</td><td rowspan="3">4</td><td>24</td><td>144</td></tr><tr><td>50/68/89</td><td>32</td><td>12</td><td>72</td></tr><tr><td>68/89/119</td><td>16</td><td>72</td><td>432</td></tr><tr><td rowspan="3">Lenslet/Sinuous</td><td>78/100/140</td><td>16</td><td>4</td><td>72</td><td>432</td></tr><tr><td colspan="2">Total LFT</td><td>8</td><td>180</td><td>1080</td></tr><tr><td>100/140/195</td><td>11.6</td><td>3</td><td>183</td><td>1098</td></tr><tr><td rowspan="3">MFT</td><td rowspan="2">MF1</td><td rowspan="2">MF2</td><td>119/166</td><td>11.6</td><td>4</td><td>244</td><td>976</td></tr><tr><td colspan="2">Total MFT</td><td>7</td><td>607</td><td>2074</td></tr><tr><td rowspan="6">HFT</td><td rowspan="3">HF1</td><td rowspan="3">HF2</td><td>195/280</td><td>6.6</td><td>1</td><td>127</td><td>508</td></tr><tr><td>235/337</td><td>6.6</td><td>1</td><td>127</td><td>508</td></tr><tr><td>402</td><td>5.7</td><td>1</td><td>169</td><td>338</td></tr><tr><td rowspan="2">Horn/OMT</td><td>HF3</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td colspan="2">Total HFT</td><td>3</td><td>423</td><td>1354</td></tr><tr><td colspan="4">Total mission</td><td>18</td><td>1210</td><td>4508</td></tr></tbody></table>

4.4.2. Focal-plane modules. The FPMs of LiteBIRD are filled with arrays of lenslet- or horn-coupled TES bolometers fabricated on silicon wafers coupled to a multiplexed readout system. The telescope designs drive the focal-plane layouts; the LFT FPU is rectangular to match the oblong illumination pattern of the crossed-Dragone telescope design, while the MFT and HFT FPUs are hexagonal arrays that pack the pixels most efficiently into the axisymmetric MFT and HFT refractive telescopes, as shown in Fig. 21. The electromagnetic coupling structures for each focal plane are based on the most mature technology for the specific frequency ranges and required bandwidths. The LFT and MFT FPMs share a common architecture of lenslet-
<figure><img src="image_24.png" /><figcaption>**Fig. 22.** *LiteBIRD* detector arrays consist of lenslet-coupled arrays for the LF- and MF-FPUs and horn-coupled detector arrays for the HF-FPU. The individual sub-figures show: (1) a single lenslet-coupled detector; (2) a photograph of a microfabricated sinuous-antenna-coupled detector; (3) a machined monolithic silicon lenslet array; (4) a microfabricated detector array in a gold-plated detector holder; (5) a single horn-coupled detector; (6) an optical micrograph of a detector with labeled components being (a) planar OMT, (b) coplanar waveguide to microstrip transition, (c) diplexer, (d) 180 hybrid, and (e) TES bolometer; (7) a photograph of a 432-element array of dichroic horn-coupled detectors and mating; and (8) a silicon platelet feedhorn array.</figcaption></figure>

coupled sinuous antennas, while the HFT FPMs use horn-coupled orthomode transducers. The dual-polarization antennas of each pixel are coupled to on-chip microstrip bandpass filters that split the signal into two or three frequency bands. The separated signals propagate along superconducting microstrip lines and thermally dissipate at TESs on thermally isolated islands for each frequency band and polarization state. TES electrical bias lines carry the induced signal to the edge of the silicon wafer where it is wire-bonded to a flexible circuit leading to the cold readout. An overview of the two detector architectures is given in Fig. 22. The TES technology is able to reach the instantaneous sensitivity required by the *LiteBIRD* mission and is a mature design technology for ground-based and sub-orbital CMB experiment heritage [223]. A demonstration of the noise-equivalent power of a prototype AlMn TES bolometer operated at 100 mK is shown in Fig. 23. The readout used for these measurements utilizes an older digital frequency-domain multiplexing (DfMux) system with SQUIDs at 4.8 K.

Cosmic-ray mitigation is integrated directly into the focal-plane design to limit cosmic-ray impacts on low-$\ell$ systematics and data loss, described in detail in Sect. 5.3.4. The transient energy deposition of cosmic rays interacting with the spacecraft can create glitches in the timestream of data sent to the readout system. It is known from the *Planck* mission that long timescale glitches are produced when cosmic rays interact with the silicon die and short pulse-like glitches result from interactions close to the thermistor [224]. This has yielded a strategy of increasing thermal conductivity between the silicon die and the focal-plane structures to reduce long timescale ther-
<figure><img src="image_25.png" /><figcaption>**Fig. 23.** Demonstration of a 100-mK TES with white noise performance in the *LiteBIRD* target range for readout and phonon noise contributions in the different frequency bands. The 0.5-pW bias power used is consistent with the lowest power band in *LiteBIRD*.</figcaption></figure>

mal fluctuations and blocking phonon propagation to the TES for the short glitches. Progress in the lab has been made in blocking the ballistic phonons near the TES by removing and adding metal layers and etching silicon. Tests with radioactive sources in the lab have shown phonon blocking effects by interrupting the phonon conduction paths to the TES [225]. The array will have dark TES channels interspersed throughout the array to help monitor and remove common-mode fluctuations in the detector responses across the wafer.

### 4.4.3. Focal-plane structures.
Each FPS contains two intermediate temperature stages at 1.8 K and 300 mK, between the FPUs at 100 mK and the 4.8-K telescope structures. A free-space low-pass edge filter and a focal-plane hood (FPH) are supported by the 1.8-K stage. An aluminized thin film spans the interstage gaps to block RF and residual warm radiation. The requirements include a thermal budget for each stage and mechanical performance to survive launch loads and keep resonances clear of the science band while in operation. Our current baseline includes aluminum, titanium, and copper metallic parts and CFRP interstage support struts. A trade-off study is in progress to determine whether struts can be designed to survive launch loads without launch locks.

### 4.5. Readout

The TES bolometers will be read out using DfMux [226]. In a DfMux system, each TES is placed in series with an inductor-capacitor (LC) bandpass filter, which separates out the individual biasing sinusoids, allowing the detectors to be operated independently (see Fig. 24). In such a system, the TES biasing voltages are provided by sinusoids at MHz frequencies. Up to 68 of these biases are summed together and transmitted to the detector array over a single set
<figure><img src="image_26.png" /><figcaption>**Fig. 24.** Schematic overview of the cryogenic readout system with digital frequency-domain multiplexing, as described in Sect. 4.5 (left) and images of a chip of 40 inductor-capacitor resonators (top right) and a single gradiometric SQUID (bottom right). The red shading indicates the portion of the circuit located at warm temperature, blue is the portion located at the sub-K temperature stages, and yellow is the twisted-pair wiring harness, which connects them. The variable resistances correspond to the TES bolometers. The nulling line shown here in the left panel uses active feedback to linearize the SQUID amplifier [175,176].</figcaption></figure>

of wires, substantially reducing the conductive heat load and enabling large TES focal planes.<fnref n="8" /> Each TES varies in resistance in response to incident radiative power, amplitude-modulating the biasing tones. Our sky signal is contained in the sidebands, analogous to the way AM radio works. The resulting current waveforms are amplified using a cryogenic SQUID array amplifier (SAA), before being transmitted to non-cryogenic electronics to be further amplified and digitally demodulated. The TES bolometers, LC resonators, SAA, and bias elements are all on the 100-mK cryogenic stage and will be discussed in Sect. 4.5.1.

The *LiteBIRD* implementation of DfMux has over a decade of development and design, spanning four separate implementations deployed on four ground-based telescopes and one balloon-borne telescope [223,175,176,226-232].

The success of DfMux is the ability to multiplex large numbers of detectors without a substantial increase in system noise, maintaining the photon-noise-limited performance of the instrument as a whole. The *LiteBIRD* design is based on, and improves upon, the design currently used in the SPT-3G (South-Pole Telescope 3rd Generation) instrument, which has demonstrated 68× multiplexing with detector-limited noise performance [230]. Section 4.5.2 describes the space-qualified implementation of the non-cryogenic portion of this system.

The overall white noise requirement of the readout system is that it should increase the fundamental statistical noise already in the detection chain by no more than 10% in each band, including yield reduction due to the readout. Other requirements are that the readout-induced crosstalk be lower than 0.3% for every bolometer, and that ambient variable magnetic fields in the spacecraft not significantly increase the noise in the detection chain.

<footnote n="8">⁸The multiplexing factor of 68× is determined largely by the cryogenic electronics design. The digital electronics and associated firmware can support up to 128× multiplexing.</footnote>
4.5.1. Cold readout. The LiteBIRD readout system is improved compared to previously fielded DfMux systems by making some modifications to the cold circuitry. The previous resistive bias element at 4 K has been changed to an inductor on the 100-mK stage and the SAA has also been moved onto the 100-mK stage.<fnref n="9" /> Since the SAAs, bias elements, and TES bolometer are in close physical proximity, parasitic inductance between the bias element and the LC filters [226] is reduced, resulting in reduced crosstalk. In addition, the reduction in parasitic inductance increases the dynamic range of the SAA SQUID elements. The reactive bias element dissipates substantially less power than the resistive bias element, enabling its placement at the 100-mK ADR-cooled stage.

System resources impose further requirements on the cold circuit: that the thermal power deposition on the 100-mK stage be less than 410 nW total; that a harness with a length of between 1.8 and 2.5 m (to be determined more precisely later) be supported by the system; and that the system has a mass less than 2 kg.

### 4.5.1.1 Bias element and LC resonator

Each bolometer is in series with a lithographed planar spiral inductor and interdigitated capacitor, which form a resonance between 1.5 MHz and 4.5 MHz and uniquely identifies the bolometer in series with it. These are fabricated lithographically and a given die will contain all 68 resonators that will be connected to a single SAA. The optimal frequency schedule balancing anticipated scatter and mechanisms of crosstalk is still under study. The LC die must also be shielded by a conductor to ensure consistent inductor values. The LC circuit-boards contain the low-impedance bias element and connect to the bolometer wafer with a superconducting strip line.

### 4.5.1.2 SQUID array amplifier and wiring harness

The SAA will be used as a low-noise transimpedance amplifier to drive the wiring harness that connects the detectors to the warm SQUID controller unit (SCU). Requirements on the SAA to 300-K harness, derived from the sensitivity requirement on the readout, are as follows. The transimpedance for the SAA-harness system must be greater than 400 Ω across the operating DfMux frequencies. The noise injected by the SAA must be such that, when integrated with the warm electronics in the detection chain, the high-level sensitivity requirement is satisfied. This requirement must be achieved including the noise-increasing effect of current sharing, which sets an upper bound on the allowable input impedance of the SAA [233]. In practice, currently demonstrated noise values of $4 \text{ pA (Hz)}^{-1/2}$ meet this requirement. Further refinement in the per-component noise injection allocation, given circuit component optimizations, are underway. Magnetic shielding of the SAAs is accomplished, as in other DfMux systems, with a hybrid system of niobium foil beneath the SAA to pin magnetic fields when in the superconducting state, and a μ-metal shield around the SAA to reduce field amplitude.

4.5.2. *Warm readout.* The LiteBIRD warm electronics (WE) implement the non-cryogenic portion of the DfMux hardware. This is divided into three separate electronics assemblies, as follows.

<footnote n="9">⁹An alternate location for the SAA under consideration is on the 350 mK stage, which has more cooling power than the 100mK stage but is still in close physical proximity to the TES bolometers and LC filters at 100mK.</footnote>
<figure><img src="image_27.png" /><figcaption>**Fig. 25.** Exploded view of the CAD model for the signal-processing unit (SPU). The signal-processing unit (SPU) contains one signal-processing assembly (SPA), on which an FPGA is mounted, and four separate digitizer assemblies. The enclosure is designed to meet thermal dissipation and vibration requirements for launch and flight environments. In total, an SPU performs the readout for 15 SQUID modules, which means up to 1020 bolometers.</figcaption></figure>

* The signal-processing assembly (SPA) contains a field-programmable gate array (FPGA) that performs the digital signal processing and communication. Each SPA supports up to 15 multiplexing modules using four digitizer assemblies. This number of a maximum of 15 SQUID modules per SPA is a design requirement, driven by a projection of the FPGA resources of radiation-hardening techniques such as triple modular redundancy (TMR), and error-correcting codes (ECC).

* The digitizer assembly (DA) performs the digital-to-analog conversion to synthesize tones, and analog-to-digital conversion to digitize the resulting waveforms. Each DA supports four multiplexing modules.

* The SQUID controller assembly (SCA) houses the SQUID biasing electronics and pre-amplification stages for the SQUID output signals. Each SCA supports four multiplexing modules.

The WE redundancy model duplicates SPA and DA electronics with “cold spares” that we can switch to in flight. They are organized in signal-processing units (SPUs) consisting of one SPA and up to four DAs, plus the enclosure (see Fig. 25). Hence there are four SPUs per telescope (two active and two cold redundant). The SCAs are much simpler, and contain only redundant elements within the electronics, rather than fully redundant spares. This WE design improves on the existing DfMUX readout [232,176] in a number of ways: the multiplexing capability per FPGA board is increased from eight multiplexing modules to 15; and the electronics is implemented with a fully radiation-qualified signal chain, including radiation-tolerant components and redundant firmware designed to be robust to the high-radiation environment. This design meets the requirements for: power consumption (approximately 80 mW per bolometer including power delivery losses and redundancy); reliability (90% confidence in sufficient yield over the mission lifetime to meet the readout-induced noise requirements); and readout noise [176].

### 4.6. Electronics architecture

The electronics architecture is designed to implement the following functions: (i) control and readout of the detectors of the three focal planes; (ii) science signal processing (cosmic-ray glitch capture and scientific signal compression); (iii) control of the cryo-coolers and ADRs;
<figure><img src="image_28.png" /><figcaption>Fig. 26. Electrical architecture.</figcaption></figure>

(iv) control of the polarization modulators of the three telescopes; (v) temperature control and monitoring of cold stages; (vi) housekeeping acquisition; and (vii) data time-tagging and subsystem synchronization.

To this purpose two mission data-processing units (MDPU-L and MDPU-MH) will central-
ize these functions for both the LFT and MHFT telescopes, respectively, as shown in Fig. 26.
They will address both the scientific signal and cooling chains, as described below.

On one hand, the scientific signal chain starts with the cold readout electronics (CRE), which is part of the focal-plane subsystem of each of the three telescopes. It then consists of the SCU, which provides bias for detectors and SQUIDs, and the warm electronics (WE), which implements the frequency-domain readout electronics. Then the mission data-processing unit (MDPU) provides the last stages of the science signal acquisition; it performs science data pre-processing, compression, detector setup algorithms, focal-plane thermal control (digital part), and subsystem synchronization. Finally, the housekeeping acquisition unit (HAU) performs the acquisition of all housekeeping that cannot be acquired inside the other subsystems. Additionally, three polarization modulation controller subsystems (PMC-L, PMC-M, and PMC-H) control the polarization modulation units of the LFT, MFT, and HFT, respectively.

On the other hand, the 0.1-K and 0.35-K ADR drivers of the cooling chain, responsible for driving the ADRs for the 0.1-K and 0.35-K stages, respectively, are connected to the MDPU-MH. The MDPU-L addresses the higher-temperature stages of the cooling chain, i.e., the 2-K JT and 4-K JT drivers (JTD), the 15-K pulse tube cooler driver, and the pre-cooler driver (PCD). The two JTDs, responsible for driving the Joule-Thomson cryo-coolers for the 1.75-
<figure><img src="image_29.png" /><figcaption>Fig. 27. Overview of the cryogenic chain.</figcaption></figure>

<figure><img src="image_30.png" /><figcaption>Fig. 28. Schematic drawing of the cryostructure and V-grooves.</figcaption></figure>

K and 4.8-K stages, provide the AC power for the ³He JT and ⁴He JT mechanical coolers, respectively, monitor the temperatures that are provided, and monitor pressures and controlling valves in the JT circuits. The PCD, which is the cooler driver for the Stirling coolers used for the shield and JT pre-cooling, provides AC power for the Stirling mechanical coolers and monitors the temperatures that they are cooling.

## 4.7. *Cryogenic system*

4.7.1. *Down to 5 K.* The cryogenic telescopes must be cooled to 4.8 K to achieve the required sensitivity. The cooling chain between 4.8 K and the warm temperature (around 300 K) is composed of passive radiative cooling and of active mechanical coolers, as illustrated in Figs. 27 and 28. The thermal architecture of *LiteBIRD* has a boundary temperature of 300 K in between the warm and cryogenic mission instruments. The cryostructure, made of CFRP, connects the 5-K interface plate and the warm temperature SVM/BUS structure, as shown in Fig. 28.

To reduce the heat loads of the shield cooler and 4-K JT, we employ large thermal shields, which are called “V-grooves”. The thermal design of *LiteBIRD* uses the radiative cooling effect as much as possible. The thermal design of the passive radiative cooler for *LiteBIRD* has been studied in Ref. [234]. The current design has three layers of V-grooves, as shown in Figs. 5 and 28. The second and third (inner) layers are cooled by the first and second stages of the shield cooler, respectively. The first (outer) layer is partially exposed to solar radiation, and therefore the surface is covered by a multilayer insulation (MLI) blanket. A Sun shield (Fig. 28) reduces the solar radiation to the outer V-groove. V-groove passive radiators are cooled down to 160, 90, and 30 K, thanks to the favorable radiative environment of the L2 orbit. Additional cooling capacity for shield cooling is provided by a mechanical cooler. A 15-K pulse-tube cooler [235] helps to decrease the temperature of the inner passive radiative enclosure to 30 K.
<figure><img src="image_31.png" /><figcaption>Fig. 29. Overview of the 5-K to 0.1-K cryogenic chain and thermal links.</figcaption></figure>

A 4-K JT and two 2ST (two-stage Stirling) pre-coolers keep the telescopes at 4.8 K. The 4-K JT cooler has a cooling capacity of 40 mW at the cold tip of 4.8 K at the EOL (end of life) [236–238]. The 2ST cooler has a cooling capacity of 200 mW at the 20-K stage at EOL [236–238]. Taking into account a 33% margin for the mechanical cooler, the available cooling power at the 4.8-K stage is 30 mW. The 4-K JT cooler and the 2ST cooler have achieved TRL 8. Based on the PLM structure, the conductive and radiative loads to the 4.8-K stage are estimated to be 13 mW. The available cooling power for the instruments, including LFT, MHFT, and the sub-kelvin coolers at 4.8 K, is 17 mW.

### 4.7.2. Below 5 K.

#### 4.7.2.1 Low-temperature thermal architecture

Both MHFT and LFT have intermediate cold stages at 1.75 K and 0.35 K between their outer bodies at 4.8 K and their detectors. In order to have continuous measurements, these intermediate stages have to be cooled continuously as well.

A solution combining a 2-K JT cooler and a sub-K (sub-kelvin) cooler with multiple ADRs has been selected to cool the instruments below 4.8 K. The two coolers are used for the two instruments, requiring a web of thermal paths, shown in Fig. 29, linking these four components. As seen in the figure, the thermal links and the sub-K cooler will be integrated on a cryomodule cooled down to 4.8 K by the 4-K JT cooler. The cryomodule is going to be located on the 4.8-K mechanical stage of the MHFT. The sub-K cooler side of the cryomodule will be placed close to the focal-plane side to minimize the thermal link lengths.

The thermal links have to be designed to minimize parasitic losses. Therefore, heat interception should be used at each of the temperature levels. Coaxial Kevlar cord supports are foreseen to be used to limit heat losses at sub-K temperatures, whereas CFRP supports will be use for both the sub-K thermal links and the 1.75-K ones. Highly conductive materials, such as copper and high-purity aluminum, will be used and superfluid heat pipes will be evaluated at 1.75 K in comparison with pure aluminum.
<figure><img src="image_32.png" /><figcaption>**Fig. 30.** Global calibration strategy. The colors of the circles give an indication of the accuracy foreseen for the related calibration operation (white indicates preliminary characterization, light blue is for verification, and dark blue identifies the phase for which the calibration will be ultimately performed). The flight calibration phase can be sub-divided into three categories: the calibration and performance verification phase prior to nominal observations; and calibration during and after the nominal observations. These are not detailed here.</figcaption></figure>

#### 4.7.2.2 2-K JT cooler

The 2-K JT cooler is provided by JAXA. It requires pre-cooling stages at 15 K and 90 K. The ³He gas is circulated by four compressors. An engineering model has been fabricated for several verification tests and has allowed this technology to achieve TRL 5 [239]. A cooling power of 10 mW at 1.75 K has been confirmed during these tests [239]. Its performance has also been demonstrated in combination with a 50 mK sub-kelvin ADR in the case of the Athena cooling chain. [240].

#### 4.7.2.3 Sub-kelvin cooler

The sub-K cooler is provided by the French Alternative Energies and Atomic Energy Commission (CEA). It works from 1.75 K to 0.1 K, as schematically shown in Fig. 29, and has been described in Ref. [241]. The 350-mK continuous cooling stage is obtained thanks to two ADR stages. Similarly, the 100-mK stage is obtained with two additional ADR stages. For low temperatures, continuous cooling is achieved using a series configuration, with one stage being at a stable temperature, while a second stage is used to extract heat from the low temperature and dump it to the highest temperature interface.

### 4.8. Calibration

4.8.1. Overall status and strategy description. The strategy of the LiteBIRD calibration is to derive a common approach for both instruments, LFT and MHFT, except for some specific items. The global picture as of today is illustrated in Fig. 30. Four steps are foreseen. The first is to characterize the performance at the component level. These characterizations are part of
the deliverables of the subsystems; they will be based on the *LiteBIRD* specifications and carried out prior to integration at the instrument level. The data from these characterizations will be used to build an instrument model and forecast the in-flight performance as we develop the system. The second step concerns beam calibration. Considering the specific related challenges (linked to the specifications on the beam knowledge and the level of accuracy required for the beam modeling), a dedicated set of measurements is foreseen, identified as “RF characterization” (cf. Sect. 4.8.2). The next step is the instrument-level calibration, which will be performed for LFT and MHFT independently, in Japan and Europe, respectively, in a cold flight-like environment. The final step of the ground activities is the final verification that will be carried out at the PLM level (system-level testing), when the LFT and MHFT will be integrated with the satellite PLM and the SVM, together with the entire *LiteBIRD* cooling system. As is highlighted in Fig. 30, it is planned that some instrumental parameters will be ultimately derived from ground-calibration operations (such as the spectral response, for instance), while, for others, the planned accuracy with flight data should allow us to rely on flight data themselves (e.g., main beam and crosstalk using planets). It is worth noting that we explore the possibility of mitigating the systematic effects through a post-analysis step and to solve for the systematic parameters as part of the map-making or component-separation processes. Nevertheless, the calibration design philosophy is to prioritize the search for a hardware mitigation solution as a starting point. The calibration plans, the error budget allocation for hardware development, and the post-flight analysis mitigation strategies will be refined as the project evolves.

In this section, we highlight the main calibration challenges, by focusing on some key parameters, namely the beams (Sect. 4.8.2), the spectral response (Sect. 4.8.3), and the polarization angle (Sect. 4.8.4). For each of them, we detail the requirements, the prospects for ground calibration and, if relevant, the plans for flight calibration. Finally, in Sect. 4.8.5, we summarize the means that we foresee to characterize the other instrumental parameters.

### 4.8.2. *Beam-pattern characterization.*
This section describes the plans foreseen for the beam-pattern calibration. The strategy relies on optical modeling, tuned and consolidated by ground measurements at various levels, from component, subsystem, instrument, and PLM levels and further fed with flight data, as schematically illustrated in Fig. 31. The cross-polar response and the far sidelobes will be characterized by a combination of ground measurements and optical modeling. The co-polar main and near-sidelobe beams are planned to be reconstructed from observations of planets.

#### 4.8.2.1 Requirements

With the example of the MHFT telescope at 100 GHz, Fig. 32 shows how each telescope element differently affects the angular regions of the co-polar beam shape. The identified angular ranges and intensity are key ingredients in the estimation of the hierarchy driving the calibration efforts. It also gives indications on the level of accuracy needed in the characterization of each individual optical element, as well as at the integrated level. Last but not least, it gives guidelines to define a suitable way of parametrizing the instrumental effects when feeding them into TOD-based simulations for systematics studies.

The derivation of the beam-calibration requirement is detailed in Sect. 5.3.3. The global requirement reads as follows: the calibration measurement uncertainty, as defined by Eq. (47),
<figure><img src="image_33.png" /><figcaption>**Fig. 31.** Beam-pattern characterization strategy, including ambient and cold calibration operations. The different levels of the operations foreseen are identified by the five columns: at component and subsystem level; at telescope level during dedicated beam-scanning campaigns; at telescope level during integrated end-to-end measurements at PLM level; and finally in flight using planets. The strong links between measurements and modeling are also shown.</figcaption></figure>

<figure><img src="image_34.png" /><figcaption>**Fig. 32.** Radiation pattern of MFT at 100 GHz for a pixel at the center of the focal plane (including the lenslet-like feed, the two lenses, the stop aperture, and the forebaffle aperture). The sharp dropoff in beam power in the 50–60° range is caused by forebaffle shielding of a Lambertian source placed at the aperture to simulate 1% large-angle scattering. The color scale indicates some qualitative aspects of the beam profile.</figcaption></figure>

should be smaller than –57 dB, when the optical response is assumed to be normalized to unity at the main peak, for a pixel of 0.5° in size.

#### 4.8.2.2 Prospects for ground calibration

As discussed above, Fig. 31 illustrates the main steps that are foreseen today for beam characterization. To meet these requirements, the plan is to rely on a very tight connection between
measurements performed both at warm and cold temperatures, together with the development of accurate software tools for instrumental modeling.

* In the first phase, the plans are to go through characterizations of subsystems (and combinations of components) at warm and cold temperatures to consolidate the design of the instrument as well as its optical modeling, allowing us to build the transfer function between warm and cold temperatures.

The MHFT BBM is an example of activities in this phase of the development plan, with comparable activities being planned for LFT. The purpose of the BBM measurement campaign is to challenge the optical modeling of the MHFT refractive designs, to assess the achievable accuracy both for the modeling and for the radio-frequency (RF) measurements, to prepare the setups that will be used for the cold measurements, and to study various effects such as, e.g., misalignment of components (tolerance analysis), standing waves, and ghosting. The BBM test plan foresees the following two models:

(a) BBM-1 (corrugated horn with one lens): simulation and characterization at MFT and HFT frequencies in different labs with a reference common channel as a cross-check. This allows for a verification of the modeling and measurement techniques and facilities.

(b) BBM-2 (corrugated horn with two lenses): increase complexity and possible evaluation of “combined” effects due to the coupling of the two lenses. This allows for a verification of the sensitivity to misalignment, AR coating, etc.

* The next step is to carry out a 2π RF characterization campaign of a representative instrument. This is the case for the 1/4-scaled model for LFT, as described in Sect. 4.2.3. The far-sidelobe pattern of the 1/4-model LFT has been measured with 1/4 wavelengths or four times higher frequencies [174]. On the MHFT side, a forthcoming optical RF demonstration model for HFT is being built and will be characterized at warm temperatures. For those measurements, dedicated compact-antenna test ranges (CATRs) are being developed both in Japan and in Europe, using broadband coherent and blackbody sources. The co- and cross-polarization responses are also assessed using a polarized source. From those measurements, the optical modeling of the instrument will be consolidated.

* A cryogenic characterization will then follow to account for the 5-K nominal working temperature of the telescopes (hence the related thermomechanical deformations), as well as for subsystems whose RF characteristics depend on temperature, such as the index of refraction of MHFT lenses for instance. This will allow us to map (within a limited angular range) the beam response using a 5-K compatible detector with a corresponding beam former. Several techniques are under study to measure the beam patterns at cryogenic temperature, e.g., near-field versus far-field using a compact antenna test range (CATR) with a continuous coherent source or with a blackbody.

* During the end-to-end calibration campaign, for which each instrument will be fully integrated and cryogenically cooled in a chamber for a characterization of in-flight-like conditions, near-field verifications are also foreseen.

* Finally, measurements of diffraction effects due to V-grooves and structures of the MHFT/LFT will be performed at the PLM level at room temperature. Those effects are expected to be small (below –60 dB from the main peak).
### 4.8.2.3 Prospects for in-flight calibration

For the main beam, as was the case for Planck [242,243], we plan to use the signals of outer planets (Mars, Jupiter, etc.) to reconstruct the most important parameters of the radiation pattern for each detector. The idea is that we can assume that a planet, given its limited angular size with respect to the FWHM of LiteBIRD's beams and its considerable brightness,<fnref n="10" /> can be considered as a bright point source that “samples” the radiation pattern $\gamma(\mathbf{r})$. With these assumptions, one can estimate the value of $\gamma(\mathbf{r})$ using

$$ \gamma(\mathbf{r}) \propto \frac{\Delta T_{\text{pl}}(\mathbf{r}) \Omega_b}{T_{\text{B,pl}} \Omega_{\text{pl}}}. \qquad (21) $$

Here $\Delta T_{\text{pl}}$ represents the component of the signal that is caused by the presence of the planet along direction $\mathbf{r}$, $\Omega_b = \int_{4\pi} \gamma(\mathbf{r}) d\Omega$ is the angular beam size, $\Omega_{\text{pl}}$ is the solid angle subtended by the planet, and $T_{\text{B,pl}}$ is the brightness temperature of the planet in the frequency band sampled by the detector.

We have used Eq. (21) to simulate how accurately we can expect to reconstruct the shape of $\gamma$, assuming that the radiation pattern has a perfectly symmetric Gaussian profile. Specifically, we simulated the scanning strategy of the LiteBIRD spacecraft and computed the amount of observation time spent on Jupiter along each direction $\mathbf{r}$ on the $4\pi$ sphere in the reference frame of the detector. To estimate $T_{\text{B,pl}}$, we have used the estimates for Jupiter's spectral energy distribution published in Refs. [244] and [245]. A plot of $\gamma(\mathbf{r})$ and the related expected error for one of the 40-GHz detectors are shown in Fig. 33.

We have fitted for the 2D Gaussian FWHM<fnref n="11" /> of the reconstructed beam pattern of 500 Monte Carlo simulations. The following assumptions have been made: (a) the nominal LiteBIRD scanning strategy parameters are used; i.e., we did not study the possibility of dedicated, deep planetary scans; (b) the mission lasts three years starting from 1 January 2027; (c) only the part of the $\gamma(\mathbf{r})$ map within three times the FWHM from the main beam axis was considered for the fit; and (d) the analysis was run for one detector at 40 GHz (LFT), one at 166 GHz (MFT), and one at 402 GHz (HFT).

The results of our simulations are reported in Table 9. All the errors are well below 1%, with the result at 402 GHz being the largest in relative terms (0.4%). The variability of the error estimates in our results<fnref n="12" /> depends on a combination of several factors: (a) the brightness temperature within the bandwidth of the detector; (b) the FWHM of the radiation pattern; and (c) the white noise level of the detector.

The estimation of the error does not take into account all sources of errors and systematic effects to be expected from real-world data. Examples include: uncertainty in background subtraction; presence of correlated noise in the timeline variability in the planetary emission; non-Gaussianities of the beams; and non-linearities and saturation of the bolometers. A rough estimation of these effects has been performed while running the same simulation code on Planck LFI data. The derived error is 2–2.5 times larger than the one quoted in Ref. [242]; therefore, we

<footnote n="10">¹⁰Jupiter, the planet with the largest apparent size, is always smaller than 0.5 arcmin, and the brightness temperature of the outer planets at the frequencies of interest for LiteBIRD are typically two orders of magnitude brighter than the CMB.</footnote>

<footnote n="11">¹¹Since the term $\Omega_b = \int_{4\pi} \gamma(\mathbf{r}) d\Omega$ in Eq. (21) depends on the unknown quantity $\gamma$, this equation should be typically solved using an iterative algorithm; we choose to neglect this complication and assume that $\Omega_b$ is perfectly known in advance.</footnote>

<footnote n="12">¹²In a real-world scenario, part of this variability could also be due to the dependence of the planetary apparent radius on the observed frequency band, at least for gaseous planets.</footnote>
<figure><img src="image_35.png" /><figcaption>**Fig. 33.** Top left: Representation of the main beam of the optical response $\gamma(r)$ for a 40-GHz LiteBIRD detector, in $(u, v)$ coordinates (in radians), used in the simulations of the in-flight beam calibration. Here $r=0$ indicates the position of the maximum amplitude of the beam pattern. Top right: Representation of the error on the beam reconstruction ($\delta\gamma$), calculated on the timespan of the LiteBIRD mission. Bottom: The quantity $\gamma/\delta\gamma$, which is the signal-to-noise ratio of the measurement on $\gamma$. The radius of the white ring is equal to the FWHM of the beam and is shown as a reference.</figcaption></figure>

can expect that a similar degradation will be experienced in the error estimates deduced from flight data.

Assuming a 2.5 degradation factor for the results in Table 9 leads to a relative error in the range 0.25–1%, where the lower bound applies to the channels dominated by cosmological signal. We expect that this error is small enough for data analysis, although a full end-to-end simulation is required to propagate the uncertainties down to the scientific products. Note that the estimation here only relies on a single source, Jupiter, and thus concatenating other planets in future analyses should give a modest improvement in the statistical error. Should the error be too large, we will consider the possibility of running dedicated observations of planets to increase the integration time.

To complete this picture, a preliminary estimation using data from *Planck* of the additional optical loading from head-on observations of Jupiter is approximately 1% at 40 GHz, 10% at 140 GHz, and 80% at 337 GHz of the expected optical loading per band. The global impact of the detector non-linearities and saturation is under study.
For the sidelobes, cross-checks between in-flight data, simulations, and ground-based characterization are foreseen, e.g., using Galactic plane crossings and studying the beam shape as a decomposition of multiple functions.

### 4.8.2.4 Beam effects coupling with other systematics

Some of the systematic effects appear as a combined effect of the beam together with other instrumental effects. Without going into full details, we briefly describe the nature of such effects.

* Frequency-dependent beam shape. This effect can be treated as a photometric gain calibration and will be discussed in a future publication. The detailed study of the photometric gain calibration requirement is described in the next section.

* Bolometer transfer function and beam shape degeneracy in the time domain. This effect is related to both the time constant and to the optical crosstalk. For the former, we expect the nominal time constant of the bolometer to be a few tens of milliseconds [222]. The two effects can be decoupled by simultaneously fitting them with planet observations, as was done for Planck [246]. For the latter, any ghosting effect due to the internal reflections within the optical system can result in an extra beam feature that is different from the designed main beam. This can be dealt with in the analysis either as an extra sidelobe feature of the beam or as crosstalk over the focal plane. We will use planetary beam observations to monitor this effect, while electrical crosstalk will be calibrated prior to flight. As such, we foresee the ability to separately assess the electrical crosstalk so that it will not be degenerate with the optically induced crosstalk.

### 4.8.3. Bandpasses.

#### 4.8.3.1 Requirements

Bandpass frequency-resolution requirements have been studied in Ref. [177], where an ideal rotating HWP has been assumed. The requirements are driven by the color-correction [247] uncertainty, that results from the calibration of the foreground signal when the CMB dipole is assumed as the photometric calibrator. With decreasing frequency-resolution of the bandpass response, the color-correction uncertainty increases. This appears clear from the expression for the color-correction factor $\gamma$:

$$ \gamma_{d,s} = \left( \frac{\int d\nu \, G(\nu) \frac{I_{d,s}(\nu)}{I_{d,s}(\nu_0)}}{\int d\nu \, G(\nu) \frac{\partial B(\nu, T)}{\partial T} \bigg|_{T_0}} \right) \frac{\partial B(\nu_0, T)}{\partial T} \bigg|_{T_0}, \quad (22) $$

where the indices “d” and “s” refer, respectively, to dust and synchrotron, $G(\nu)$ is the bandpass function, $I_d(\nu)$ ($I_s(\nu)$) is the dust (synchrotron) spectrum, $\nu_0$ is the effective central frequency of the given band, $B(\nu, T)$ is the blackbody spectrum, and $T_0$ is the CMB temperature.

In Ref. [177] the color-correction uncertainty resulting from a given finite spectral resolution of the bandpass response has been propagated to a bias on the reconstructed tensor-to-scalar ratio $r$ for all LiteBIRD bands. The results show that the high-frequency channels drive the requirements due to the relative brightness of the dust signal.

In Fig. 34 we illustrate the worst-case scenario, which corresponds to a top-hat bandpass (with 30% bandwidth) for the 337-GHz channel and show the color-correction uncertainty as a function of the frequency resolution. The requirement (red dashed line) is found by imposing the resulting tensor-to-scalar ratio bias (after component separation) to be $\le 5.7 \times 10^{-6}$ and
<figure><img src="image_36.png" /><figcaption>**Fig. 34.** Bandpass and color correction. Left: Top-hat bandpass response (in solid blue) at 337 GHz with 30% bandwidth. A resampling process with 1-GHz resolution is also shown in orange. Right: Calculation of the color-correction error for dust ($\delta\gamma_d$) as a function of decreasing resolution for the bandpass response on the left. The blue solid line represents the rms value for 100 realizations of the resampling process with a given resolution, while the orange solid line represents the maximum value among 100 realizations. The requirement is shown by the red dashed line. Figure from Ref. [177].</figcaption></figure>

corresponds to 0.2 GHz. The complete analysis shows that the spectral resolution should be in the range $\Delta\nu \simeq 0.2-2$ GHz, depending on the mean frequency of the band.

The detailed allocations from the current requirement to each hardware component are yet to be assigned. Comprehensive studies of the requirements, including the effects of more complicated foregrounds such as CO lines, are beyond the scope of this paper.

### 4.8.3.2 Prospects for ground calibration

For reference purposes in terms of achievable accuracy for the calibration of a CMB instrument in a space environment, we can consider the High Frequency Instrument of Planck (Planck-HFI). The resolution on the reconstruction of the mean frequency of the bandpass was between 0.56 GHz at 100 GHz and 1.57 GHz at 545 GHz, while the bandwidth accuracy was between 0.4 GHz and 3.1 GHz, and the point-per-point spectral resolution of the measurements was sub-GHz [248]. Still, uncertainties in the signal-to-noise (S/N) ratio achieved in these measurements were set by the limitations of the reference detector used in the calibration facility (see Ref. [249] for a description of the facility). This limitation (especially in the lowest-frequency channel, 100 GHz) placed a tension between binning the spectral measurements to gain S/N against having a higher spectral resolution knowledge used in the removal of specific spectral features (such as CO). The strategy for LiteBIRD is slightly different. At the component level, the spectral response characterization is planned to be performed using a vector network analyzer (VNA) with extremely high spectral resolution in order to characterize the potential presence of inherent fringes. At the instrument level, spectral measurements are part of the datacube reconstruction (cf. Sect. 4.8.4), which should allow us to achieve the required sub-GHz resolution. In addition, the out-of-band rejection (particularly important for component separation), which could be characterized down to levels of $10^{-12}$, as was done for the Planck-HFI filter chains [248], will be reconstructed using a combination of component-level and end-to-end cryogenic tests.

### 4.8.4. Polarization angle.
In this section, we address the calibration of the polarization angle for LiteBIRD.
### 4.8.4.1 Requirements

The derivation of the requirements on the relative and absolute polarization angles follows Ref. [250]. It is driven by the bias on $r$ produced by the miscalibration of polarization angles, taking into account the component-separation process. Assuming a given correlation coefficient matrix $\rho_{v_1 v_2}$ for the angle offset (either relative or absolute angles) of the frequency detector sets $v_1$ and $v_2$, it can be shown that the bias on $r$ is related to that matrix by the following expression:

$$ \langle \delta_r \rangle \approx c^2 A \left( \sum_{\ell=2}^{\ell_{\max}} H_{\ell} \right) \left( \sum_{v_1=1}^{N_{\text{elem}}} \sum_{v_2=1}^{N_{\text{elem}}} \rho_{v_1, v_2} \right), \quad (23) $$

where

$$ A = 4 \left[ \sum_{\ell=2}^{\ell_{\max}} \frac{(B_{\ell}^{\text{fid}})^2}{\text{Var}(B_{\ell})} \right]^{-1}, \quad (24) $$

$$ H_{\ell} = \frac{E_{\ell} B_{\ell}^{\text{fid}}}{\text{Var}(B_{\ell})}, \quad (25) $$

in which $B_{\ell}^{\text{fid}}$ and $B_{\ell}$ are the fiducial and observed B-mode power spectra, respectively, and $E_{\ell}$ is the fiducial E-mode power spectrum. Equation (23) provides the requirements on the polarization angle accuracy $\sigma_{\alpha_v}$ assuming a bias of 1% of the systematics budget in the $r$ parameter.

The requirements on the relative angles refer to the $N_{\text{elem}} = 22$ frequency elements that are included in the three focal planes of the LFT, MFT, and HFT (see Sect. 5.1). The following cases are considered:

* Case 0: all 22 elements are uncorrelated, except those within the same telescope, which are fully correlated;

* Case 1: all 22 elements are fully correlated;

* Case 2: all 22 elements are partially correlated ($\rho_{v_1, v_2} = 0.5$, for any $v_1 \neq v_2$), except those within the same telescope, which are fully correlated;

* Case 3: all 22 elements are uncorrelated (the most ideal case).

The 22 elements correspond to the frequency bands per telescope and per detector pixel size, as listed in Table 3. The results of the relative angle requirements for each of these correlation cases are given in Fig. 35 (left panel).

The requirements on the absolute angle consist of a global offset, which accounts for the mismatch between the SVM and the PLM, and three additional ones that account for the mismatch between the PLM and each of the three focal planes. The following cases have been considered:

* Case 0: no correlations;

* Case 1: the four offsets are fully correlated;

* Case 2: the global offset is uncorrelated with any of the three focal-plane offsets, and the latter ones are fully correlated.

The corresponding requirements are given in Fig. 35 (right panel). They appear less stringent for the high-frequency channels, as opposed to the case of most of the other systematics effects, like, for instance, the beam knowledge requirement, which is more stringent at high frequency, mainly because of the effect of the higher resolution in these bands.
<figure><img src="image_37.png" /><figcaption>Fig. 35. Left: Required knowledge of the relative polarization angle for the 22 frequency elements within the LFT (black and green), MFT (blue), HFT (red), and the four correlation cases considered: 0 (square); 1 (circle); 2 (diamond); and 3 (triangle). Right: Required knowledge of the absolute polarization angle for the four offsets and the three correlation cases considered: 0 (square); 1 (circle); and 2 (triangle). “GLOBAL” stands for the combination of all channels.</figcaption></figure>

### 4.8.4.2 Prospects for in-flight calibration using EB cross-correlation

For the in-flight absolute angle calibration, we use the methodology of Refs. [251–253], which showed that we can calibrate the miscalibration angle, $\alpha$, using the observed power spectra, including both the CMB and the foreground, using full-sky maps. The basic idea is to use the relation between the observed (“o”) EB cross correlation and the difference of EE and BB power spectra as

$$ \langle C_{\ell}^{EB,o} \rangle = \frac{\tan(4\alpha)}{2} (\langle C_{\ell}^{EE,o} \rangle - \langle C_{\ell}^{BB,o} \rangle) + \langle C_{\ell}^{EB} \rangle, \quad (26) $$

where $\langle C_{\ell}^{EB} \rangle$ is the ensemble average of the intrinsic EB cross-correlation, which has been assumed to be zero both for the CMB and the foregrounds. It was shown that we can calibrate the LiteBIRD detectors’ absolute polarization angle with uncertainties of <2.7 arcmin [253].

As part of the feasibility demonstrations, a blind analysis was performed using sky maps that were simulated with a polarization angle offset. This study, summarized in Ref. [254], showed that the offset angles could be recovered by imposing the null detection of $C_{\ell}^{EB}$ using two different analyses.

This way of calibrating angles, called “self-calibration” [255], eliminates LiteBIRD’s ability to probe new parity-violating physics using the cosmological EB correlation. The potential presence of the EB correlation intrinsic to the Galactic foreground emission, which is yet to be found [60,78,256,257], could complicate the analysis further. The method of Ref. [251] can mitigate these complications, restoring LiteBIRD’s ability to probe new physics and account for possible foreground EB signals (see Sect. 6.2).

### 4.8.4.3 Prospects for in-flight calibration using the Crab Nebula

The Crab Nebula (Tau A) is one of the brightest compact sources in the sky in the microwave range, and the brightest one in polarization. For this reason, it has been used to calibrate CMB experiments, and is specifically the main target on the sky used to calibrate the polarization direction (together with the $C_{\ell}^{EB}$ technique). Interestingly, recent measurements show a discrepancy of $\simeq 1^{\circ}$ between the polarization direction derived through the $C_{\ell}^{EB}$ method and through the use of the Crab [258,259]).

Table 10 shows LiteBIRD’s expected sensitivities on the measurement of the Crab polarization angle. To obtain these values we have used: (i) a model for the polarization spectrum
<table><caption>**Table 9.** Estimated error on the reconstruction of the FWHM of the radiation pattern for three *LiteBIRD* detectors.</caption><thead><tr><td>Detector</td><td>Error [arcmin]</td></tr></thead><tbody><tr><td>LFT (40 GHz)</td><td>0.09</td></tr><tr><td>MFT (166 GHz)</td><td>0.03</td></tr><tr><td>HFT (402 GHz)</td><td>0.07</td></tr></tbody></table>

<table><caption>**Table 10.** Expected *LiteBIRD* sensitivity (statistical errors) on the measurement of the Crab Nebula polarization angle ($\Delta\gamma$), per individual bolometer, and when all bolometers in each frequency band are combined.</caption><thead><tr><th rowspan="2">Frequency [GHz]</th><th colspan="2">Δγ (arcmin)</th></tr><tr><th>Per frequency band</th><th>Per detector</th></tr></thead><tbody><tr><td>40</td><td>2.7</td><td>21</td></tr><tr><td>50</td><td>2.2</td><td>18</td></tr><tr><td>60</td><td>2.6</td><td>21</td></tr><tr><td>68</td><td>1.8</td><td>21</td></tr><tr><td>78</td><td>1.8</td><td>21</td></tr><tr><td>89</td><td>1.7</td><td>21</td></tr><tr><td>100</td><td>1.1</td><td>14</td></tr><tr><td>119</td><td>1.0</td><td>12</td></tr><tr><td>140</td><td>1.2</td><td>14</td></tr><tr><td>166</td><td>2.0</td><td>45</td></tr><tr><td>195</td><td>2.5</td><td>48</td></tr><tr><td>235</td><td>4.9</td><td>79</td></tr><tr><td>280</td><td>5.6</td><td>89</td></tr><tr><td>337</td><td>6.1</td><td>98</td></tr><tr><td>402</td><td>7.1</td><td>130</td></tr></tbody></table>

$S(\nu) = 79.0(\nu/1 \text{ GHz})^{-0.35}$ [260], and a value of the Crab's secular decrease of $-0.218\% \text{yr}^{-1}$, derived from WMAP data [261]; and (ii) *LiteBIRD* mission nominal sensitivities, and a simulation of the satellite scanning strategy that gives the expected integration time at the position of the source. As can be seen in Table 10, at the best frequencies the polarization angle of Tau A will be measured with an accuracy of $\simeq 1$ arcmin. For comparison, the error in the Planck-HFI measurement was $\simeq 5$ arcmin [262].

Table 10 shows that *LiteBIRD* will be able to measure the polarization angle of the Crab with a statistical error that is comparable with the requirement (see Fig. 35), after integration of all detectors in each frequency band. The error per detector is, however, far from the requirement, and therefore precise relative calibration between detectors must be achieved by alternative techniques like ground-based calibration (see below).

An important caveat is that, in this regime of very good statistical accuracy, the error budget will be fully dominated by the uncertainty in the model giving Crab's polarization angle. Currently, the best measurements have statistical errors of $\simeq 0.5^{\circ}$ [260,262,263]. However, these observations are dominated by systematic uncertainties, which boost the global error up to $>1^{\circ}$ [264]. Recently Ref. [260] presented a new measurement at 150 GHz obtained with the NIKA camera mounted on the IRAM 30-m telescope. After combination with previous mea-