# Spectral distortions of the CMB as a probe of inflation, recombination, structure formation and particle physics

J. Chluba, A. Kogut, S.P. Patil, M.H. Abitbol, N. Aghanim, Y. Ali-Haïmoud, M.A. Amin, J. Aumont, N. Bartolo, K. Basu, et al.

► To cite this version:

J. Chluba, A. Kogut, S.P. Patil, M.H. Abitbol, N. Aghanim, et al. Spectral distortions of the CMB as a probe of inflation, recombination, structure formation and particle physics: Astro2020 Science White Paper. Bull.Am.Astron.Soc., 2019, 51 (3), pp.184. hal-02123336

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<figure><img src="image_1.png" /></figure>

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# Astro2020 Science White Paper
## Spectral Distortions of the CMB as a Probe of Inflation, Recombination, Structure Formation and Particle Physics

**Primary thematic area:** Cosmology and Fundamental Physics

**Secondary thematic area:** Galaxy Evolution

**Corresponding author email:** Jens.Chluba@Manchester.ac.uk

J. Chluba<fnref n="1" />, A. Kogut<fnref n="2" />, S. P. Patil<fnref n="3" />, M. H. Abitbol<fnref n="4" />, N. Aghanim<fnref n="5" />, Y. Ali-Haïmoud<fnref n="6" />, M. A. Amin<fnref n="7" />,
J. Aumont<fnref n="8" />, N. Bartolo<fnref n="9" />,<fnref n="10" />,<fnref n="11" />, K. Basu<fnref n="12" />, E. S. Battistelli<fnref n="13" />, R. Battye<fnref n="1" />, D. Baumann<fnref n="14" />, I. Ben-Dayan<fnref n="15" />,
B. Bolliet<fnref n="1" />, J. R. Bond<fnref n="16" />, F. R. Bouchet<fnref n="17" />, C. P. Burgess<fnref n="18" />,<fnref n="19" />, C. Burigana<fnref n="20" />,<fnref n="21" />,<fnref n="22" />, C. T. Byrnes<fnref n="23" />,
G. Cabass<fnref n="24" />, D. T. Chuss<fnref n="25" />, S. Clesse<fnref n="26" />,<fnref n="27" />, P. S. Cole<fnref n="23" />, L. Dai<fnref n="28" />, P. de Bernardis<fnref n="13" />,<fnref n="29" />, J. Delabrouille<fnref n="30" />,<fnref n="31" />,
V. Desjacques<fnref n="32" />, G. de Zotti<fnref n="11" />, J. A. D. Diacoumis<fnref n="33" />, E. Dimastrogiovanni<fnref n="34" />,<fnref n="35" />, E. Di Valentino<fnref n="1" />,
J. Dunkley<fnref n="36" />, R. Durrer³⁷, C. Dvorkin³⁸, J. Ellis³⁹, H. K. Eriksen⁴⁰, M. Fasiello⁴¹, D. Fixsen⁴², F. Finelli⁴³,
R. Flauger⁴⁴, S. Galli⁴⁵, J. Garcia-Bellido⁴⁶, M. Gervasi⁴⁷, V. Gluscevic<fnref n="36" />,⁴⁸, D. Grin⁴⁹, L. Hart<fnref n="1" />,
C. Hernández-Monteagudo⁵⁰, J. C. Hill<fnref n="28" />,⁵¹, D. Jeong⁵²,⁵³, B. R. Johnson⁵⁴, G. Lagache⁵⁵, E. Lee<fnref n="1" />,
A. Lewis<fnref n="23" />, M. Liguori<fnref n="9" />,<fnref n="10" />,<fnref n="11" />, M. Kamionkowski⁵⁷, R. Khatri⁵⁸, K. Kohri⁵⁹, E. Komatsu<fnref n="24" />, K. E. Kunze⁵⁹,
A. Mangilli⁶⁰, S. Masi<fnref n="13" />,<fnref n="29" />, J. Mather<fnref n="2" />, S. Matarrese<fnref n="9" />,<fnref n="10" />,<fnref n="11" />,⁶¹, M. A. Miville-Deschênes⁶², T. Montaruli⁶³,
M. Münchmeyer<fnref n="19" />, S. Mukherjee⁴⁵,⁶⁴, T. Nakama⁶⁵, F. Nati⁴⁷, A. Ota⁶⁶, L. A. Page<fnref n="36" />, E. Pajer⁶⁷,
V. Poulin⁵⁶,⁶⁸, A. Ravenni<fnref n="1" />, C. Reichardt⁶⁹, M. Remazeilles<fnref n="1" />, A. Rotti<fnref n="1" />, J. A. Rubiño-Martin⁷⁰,⁷¹,
A. Sarkar<fnref n="1" />, S. Sarkar⁷², G. Savini⁷³, D. Scott⁷⁴, P. D. Serpico⁷⁵, J. Silk⁵⁶,⁷⁶, T. Souradeep⁷⁷,
D. N. Spergel⁵¹,⁷⁸, A. A. Starobinsky⁷⁹, R. Subrahmanyan⁸⁰, R. A. Sunyaev<fnref n="24" />, E. Switzer<fnref n="2" />, A. Tartari⁸¹,
H. Tashiro⁸², R. Basu Thakur⁸³, T. Trombetti<fnref n="20" />, B. Wallisch<fnref n="28" />,⁴⁴, B. D. Wandelt⁴⁵, I. K. Wehus⁴⁰,
E.J. Wollack<fnref n="2" />, M. Zaldarriaga<fnref n="28" />, M. Zannoni⁴⁷

**Additional endorsers:** www.Chluba.de/SDWP-Decadal-2020/Endorsers.pdf

<footnote n="1">¹ Jodrell Bank Centre for Astrophysics, School of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, U.K.</footnote>

<footnote n="2">² NASA/GSFC, Mail Code: 665, Greenbelt, MD 20771, USA</footnote>

<footnote n="3">³ Niels Bohr International Academy and Discovery Center, Blegdamsvej 17, 2100 Copenhagen, Denmark</footnote>

<footnote n="4">⁴ University of Oxford, Denys Wilkinson Building, Keble Road, Oxford, OX1 3RH, UK</footnote>

<footnote n="5">⁵ Institut d'Astrophysique Spatiale (IAS), CNRS (UMR8617), Université Paris-Sud, Batiment 121, 91405 Orsay, France</footnote>

<footnote n="6">⁶ Center for Cosmology and Particle Physics, Department of Physics, New York University, New York, NY 10003, USA</footnote>

<footnote n="7">⁷ Department of Physics and Astronomy, Rice University, 6100 Main Street, Houston, Texas 77005, USA</footnote>

<footnote n="8">⁸ IRAP, Université de Toulouse, CNRS, CNES, UPS, France</footnote>

<footnote n="9">⁹ Dipartimento di Fisica e Astronomia 'Galileo Galilei', Universita' degli Studi di Padova, via Marzolo 8, I-35131, Padova, Italy</footnote>

<footnote n="10">¹⁰ INFN, Sezione di Padova, via Marzolo 8, I-35131, Padova, Italy</footnote>

<footnote n="11">¹¹ INAF-Osservatorio Astronomico di Padova, Vicolo dell'Osservatorio 5, I-35122 Padova, Italy</footnote>

<footnote n="12">¹² Argelander-Institut für Astronomie, Universität Bonn, Auf dem Hügel 71, D-53121 Bonn, Germany</footnote>

<footnote n="13">¹³ Physics department, Sapienza University of Rome, Piazzale Aldo Moro 5, 00185, Rome, Italy</footnote>

<footnote n="14">¹⁴ Institute for Theoretical Physics, University of Amsterdam, Science Park 904, Amsterdam, 1098 XH, The Netherlands</footnote>

<footnote n="15">¹⁵ Physics Department, Ariel University, Ariel 40700, Israel</footnote>

<footnote n="16">¹⁶ Canadian Institute for Theoretical Astrophysics, 60 St. George Street, University of Toronto, Toronto, ON, M5S 3H8, Canada</footnote>

<footnote n="17">¹⁷ Institut d'Astrophysique de Paris, UMR7095, CNRS & Sorbonne Université, 98 bis Boulevard Arago, F-75014, Paris, France</footnote>

<footnote n="18">¹⁸ McMaster University, 1280 Main St W, Hamilton, ON L8S 4L8, Canada</footnote>

<footnote n="19">¹⁹ Perimeter Institute, 31 Caroline Street North, Waterloo, Ontario, N2L 2Y5, Canada</footnote>

<footnote n="20">²⁰ INAF, Istituto di Radioastronomia, Via Piero Gobetti 101, I-40129 Bologna, Italy</footnote>

<footnote n="21">²¹ Dipartimento di Fisica e Scienze della Terra, Università di Ferrara, Via Giuseppe Saragat 1, I-44122 Ferrara, Italy</footnote>

<footnote n="22">²² Istituto Nazionale di Fisica Nucleare, Sezione di Bologna, Via Irnerio 46, I-40126 Bologna, Italy</footnote>

<footnote n="23">²³ Department of Physics and Astronomy, University of Sussex, Brighton BN1 9QH, United Kingdom</footnote>

<footnote n="24">²⁴ Max-Planck-Institut für Astrophysik, 85741 Garching, Germany</footnote>

<footnote n="25">²⁵ Department of Physics, Villanova University, 800 E. Lancaster Ave., Villanova, PA 19085</footnote>

<footnote n="26">²⁶ IRMP, CURL group, Louvain University, 2 Chemin du Cyclotron, 1348 Louvain-la-Neuve, Belgium</footnote>

<footnote n="27">²⁷ Namur Institute of Complex Systems, Department of Mathematics, University of Namur, Rempart de la Vierge 8, 5000 Namur, Belgium.</footnote>

<footnote n="28">²⁸ Institute for Advanced Study, Princeton, NJ 08540, USA</footnote>

<footnote n="29">²⁹ INFN sezione di Roma, P.le A. Moro 2, 00815 Roma, Italy</footnote>

<footnote n="30">³⁰ Laboratoire Astroparticule et Cosmologie (APC), CNRS/IN2P3, 10, rue Alice Domon et Léonie Duquet, 75205 Paris Cedex 13, France</footnote>

<footnote n="31">³¹ Département d'Astrophysique, CEA Saclay DSM/Irfu, 91191 Gif-sur-Yvette, France</footnote>

<footnote n="32">³² Physics Department and Asher Space Science Institute, Technion, Haifa 3200003, Israel</footnote>

<footnote n="33">³³ School of Physics, The University of New South Wales, Sydney NSW 2052, Australia</footnote>

<footnote n="34">³⁴ Department of Physics/CERCA/Institute for the Science of Origins, Case Western Reserve University, Cleveland, OH 44106-7079, USA</footnote>

<footnote n="35">³⁵ School of Physics, The University of New South Wales, Sydney NSW 2052, Australia</footnote>

<footnote n="36">³⁶ Joseph Henry Laboratories of Physics, Jadwin Hall, Princeton University, Princeton, NJ 08544, USA</footnote>
³⁷ Department de Physique Theorique, Université de Genève, Quai E. Ansermet 24, 1211 Genève, Switzerland

³⁸ Department of Physics, Harvard University, Cambridge, MA, 02138, USA

³⁹ Department of Physics, Kings College London, London WC2R 2LS, UK

⁴⁰ Institute of Theoretical Astrophysics, University of Oslo, P.O. Box 1029 Blindern, N-0315 Oslo, Norway

⁴¹ Institute of Cosmology and Gravitation, University of Portsmouth, Dennis Sciama Building, Burnaby Road, PO1 3FX, U.K

⁴² Department of Astronomy, University of Maryland, College Park, MD 20742-2421, USA

⁴³ INAF - Osservatorio di Astrofisica e Scienza dello Spazio, Via Gobetti 101, I-40129 Bologna, Italy

⁴⁴ Department of Physics, University of California San Diego, 9500 Gilman Drive #0319, La Jolla CA 92093, USA

⁴⁵ Sorbonne Université, CNRS, UMR 7095, Institut d'Astrophysique de Paris, 98 bis bd Arago, 75014 Paris, France

⁴⁶ Instituto de Física Teórica UAM/CSIC, Universidad Autónoma de Madrid, 28049 Madrid, Spain

⁴⁷ Physics Department, University of Milano Bicocca, 20126, Piazza della Scienza 3, Milano

⁴⁸ Department of Physics, University of Florida, Gainesville, FL 32611

⁴⁹ Haverford College, 370 Lancaster Ave, Haverford PA, 19041, USA

⁵⁰ Centro de Estudios de Física del Cosmos de Aragón (CEFCA), Plaza San Juan, 1, planta 2, E-44001, Teruel

⁵¹ Center for Computational Astrophysics, Flatiron Institute, 162 5th Avenue, New York, NY 10010, USA

⁵² Department of Astronomy and Astrophysics, The Pennsylvania State University, University Park, PA 16802, USA

⁵³ Institute for Gravitation and the Cosmos, The Pennsylvania State University, University Park, PA 16802, USA

⁵⁴ Department of Physics, Columbia University, 538 West 120th Street 1122 Pupin Hall, Box 28, MC 5228 New York, NY 10027, USA

⁵⁵ Aix Marseille Univ, CNRS, CNES, LAM, Marseille, France

⁵⁶ Department of Physics and Astronomy, The Johns Hopkins University, 3701 San Martin Drive, Baltimore MD 21218, USA

⁵⁷ Department of Theoretical Physics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India

⁵⁸ KEK and Sokendai, Tsukuba 305-0801, Japan

⁵⁹ Departamento de Física Fundamental, Universidad de Salamanca, Plaza de la Merced s/n, 37008 Salamanca, Spain

⁶⁰ Institut de Recherche en Astrophysique et Planetologie (IRAP), CNRS, 9 avenue du Colonel Roche 31028 Toulouse, France

⁶¹ Gran Sasso Science Institute (GSSI) Viale Francesco Crispi 7, I-67100 L'Aquila, Italy

⁶² AIM, CEA, CNRS, Université Paris-Saclay, Université Paris Diderot, Sorbonne Paris Cité, F-91191 Gif-sur-Yvette, France

⁶³ Département de physique nucléaire et corpusculaire, Université de Genève, 24 Quai Ernest-Ansermet, 1205 Genève 4, Suisse

⁶⁴ Sorbonne Universites, Institut Lagrange de Paris, 98 bis Boulevard Arago, 75014 Paris, France

⁶⁵ Jockey Club Institute for Advanced Study, The Hong Kong University of Science and Technology, Hong Kong, P.R. China

⁶⁶ Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, CB3 0WA, UK

⁶⁷ DAMTP, Centre for Mathematical Sciences, University of Cambridge, CB3 0WA, UK

⁶⁸ LUPM, CNRS & Université de Montpellier (UMR-5299), Place Eugène Bataillon, F-34095 Montpellier Cedex 05, France

⁶⁹ School of Physics, University of Melbourne, Parkville VIC 3010, Australia

⁷⁰ Instituto de Astrofísica de Canarias, E-38200 La Laguna, Tenerife, Spain

⁷¹ Departamento de Astrofísica, Universidad de La Laguna, E-38206 La Laguna, Tenerife, Spain

⁷² University of Oxford, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, UK

⁷³ Physics & Astronomy Dept., UCL, London WC1E 6BT, UK

⁷⁴ Department of Physics & Astronomy, University of British Columbia, 6224 Agricultural Road, Vancouver, British Columbia, 55 Canada

⁷⁵ Université Grenoble Alpes, USMB, CNRS, LAPTh, F-74940 Annecy, France

⁷⁶ Department of Physics and Beecroft Inst. for Particle Astrophysics and Cosmology, University of Oxford, 1 Keble Road, Oxford, OX1 3RH, UK

⁷⁷ IUCAA, Post Bag 4 Ganeshkhind, Pune 411007, India

⁷⁸ Department of Astrophysical Sciences, Peyton Hall, Princeton University, Princeton, NJ 08544, USA

⁷⁹ L. D. Landau Institute for Theoretical Physics RAS, Moscow 119334, Russia

⁸⁰ Raman Research Institute, C V Raman Avenue, Sadashivanagar, Bangalore 560080, India

⁸¹ INFN Sezione di Pisa Largo B. Pontecorvo 3, Edif. C I-56127 Pisa, Italy

⁸² Division of Particle and Astrophysical Science, Graduate School of Science, Nagoya University, Chikusa, Nagoya 464-8602, Japan

⁸³ Department of Physics, California Institute of Technology, Pasadena, California 91125, USA
## EXECUTIVE SUMMARY

Following the pioneering observations with COBE in the early 1990s, studies of the cosmic microwave background (CMB) have focused on temperature and polarization anisotropies. CMB spectral distortions – tiny departures of the CMB energy spectrum from that of a perfect blackbody – provide a second, independent probe of fundamental physics, with a reach deep into the primordial Universe. The theoretical foundation of spectral distortions has seen major advances in recent years, which highlight the immense potential of this emerging field. Spectral distortions probe a fundamental property of the Universe – its *thermal history* – thereby providing additional insight into processes within the cosmological standard model¹ (CSM) as well as new physics beyond. Spectral distortions are an important tool for understanding inflation and the nature of dark matter. They shed new light on the physics of recombination and reionization, both prominent stages in the evolution of our Universe, and furnish critical information on baryonic feedback processes, in addition to probing primordial correlation functions at scales inaccessible to other tracers. In principle the range of signals is vast: *many orders of magnitude of discovery space* could be explored by detailed observations of the CMB energy spectrum. Several CSM signals are predicted and provide clear experimental targets, some of which are already observable with present-day technology. Confirmation of these signals would extend the reach of the CSM by orders of magnitude in physical scale as the Universe evolves from the initial stages to its present form. *The absence of these signals would pose a huge theoretical challenge, immediately pointing to new physics.*

## I. COSMOLOGY BEYOND THERMAL EQUILIBRIUM

Cosmology is now a precise scientific discipline, with detailed theoretical models that fit a wealth of very accurate measurements. Of the many cosmological data sets, the CMB temperature and polarization anisotropies provide the most stringent and robust constraints on theoretical models, allowing us to determine the key parameters of our Universe (e.g., the total density, expansion rate and baryon content) with unprecedented precision, while simultaneously addressing fundamental questions about inflation and early-universe physics. By studying the statistics of the CMB anisotropies with different experiments over the past decades we have entered the era of precision cosmology, clearly establishing the highly-successful ΛCDM concordance model [1–3].

But the quest continues. Despite its many successes, ΛCDM is *known to be incomplete*. It traces the growth of structure in the Universe from primordial density perturbations to the modern era, but the origin of those perturbations remains poorly understood. In addition, in spite of relentless efforts, the nature of dark matter (DM) and dark energy remains a mystery. Together, these enigmatic components comprise 95% of the energy density of the Universe. Particle and high-energy physics offer candidate solutions of these problems (e.g., inflation and particle dark matter), but these inevitably require new physics beyond the Standard Model of particle physics.

*Precision measurements of the CMB energy spectrum open a new window into the physics of the early Universe, constraining models in ways not possible using other techniques.* Departures of the CMB energy spectrum from a pure blackbody – commonly referred to as *spectral distortions* – encode unique information about the thermal history of the Universe, from when it was a few months old until today. Since the measurements with COBE/FIRAS in the early ’90s, the sky-averaged CMB spectrum is known to be extremely close to a perfect blackbody at a temperature $T_0 = (2.7255\pm0.0006)$ K [4, 5], with possible distortions limited to one part in $10^5$. This impressive measurement was awarded the 2006 Nobel Prize in Physics and already rules out cosmologies with extended periods of large energy release.

Spectral distortions are created by processes that drive matter and radiation out of thermal equilibrium after thermalization becomes inefficient at redshift $z \lesssim 2 \times 10^6$. Exam-
ples are energy-releasing mechanisms that heat the baryonic matter, inject photons or other electromagnetically-interacting particles. The associated signals are usually characterized as μ- and y-type distortions, formed by energy exchange between electrons and photons through Compton scattering [6–10]. Compton scattering is inefficient at $z \lesssim 5 \times 10^4$, yielding a y-type distortion, which probes the thermal history during recombination and reionization (Fig. 1).

In contrast, a μ-type (or chemical potential) distortion forms at $z \gtrsim 5 \times 10^4$, when Compton scattering is very efficient. A μ-distortion cannot be generated at recent epochs and thus directly probes events in the pre-recombination era.

The simple classical picture has been refined in recent years. We now understand that the transition between μ- and y-type distortions is gradual and that the signal contains additional time-dependent information [11–13]. This extra information is contained in the residual or *r*-type distortion and can be used to distinguish energy release mechanisms [14, 15]. Distortions created by photon-injection mechanisms exhibit rich spectral phenomena

[16], one prominent example being the distortion created by the cosmological recombination process [17–19] (see Fig. 1). Additional information can be imprinted by non-equilibrium processes in the pre-recombination hydrogen and helium plasma [20–22] or by non-thermal particles in high-energy particle cascades [e.g., 16, 22–25]. Finally, distortion anisotropies are expected and can be correlated against tracers of both primordial density perturbations and large-scale structure to further probe cosmic evolution [26–31].

Spectral distortions thus provide more than just a simple integral constraint for cosmology. They are a unique and powerful probe of a wide range of interactions between particles and CMB photons, reaching back all the way from the present to a few months after the Big Bang and allowing us to access information that cannot be extracted in any other way. Broad overviews of the CMB spectral distortion science case can be found in [11, 18, 32–38].

<figure><img src="image_2.png" /><figcaption>**FIG. 1:** Evolution of spectral distortions across time. Distortions probe the thermal history over long periods deep into the primordial Universe that are inaccessible by other means.</figcaption></figure>

## II. PHYSICS BEYOND ΛCDM AND THE STANDARD MODEL

A central question in modern cosmology is the origin of the observed primordial density perturbations. Measurements from CMB anisotropies and large-scale structure find a nearly scale-invariant power spectrum $P(k) \simeq k^{n_s-1}$ with spectral index $n_s = 0.965 \pm 0.004$, sampled over a range of spatial scales $k \simeq 10^{-4}$ to $0.1 \text{ Mpc}^{-1}$ [39]. Their phase coherence is evidence for their super-Hubble nature, and their near scale-invariance is evidence of a weakly broken shift symmetry in the underlying theory. However, their precise origin is as of yet unknown. Inflation provides a widely accepted framework [40–43], with the simplest models generically predicting a small departure from scale-invariance (with $n_s < 1$) as the inflaton rolls down its potential [44–47]. However, various alternatives to inflation have been proposed [48–57] and no clear theoretical consensus has yet emerged. Searches for a B-mode pattern in CMB polarization could yield compelling evidence
for the simplest inflationary models. CMB polarization measurements so far only provide upper limits [58, 59] with no firm target from theory for a guaranteed detection. However, detection of a tensor to scalar ratio of $r \approx 10^{-3}$ is a distinguishing benchmark for large-field models, which in certain realizations further manifest the specific relation $r \approx (1 - n_s)^2$ [e.g., 40, 60].

Spectral distortions provide a unique new probe of primordial density perturbations. Inflation may or may not be a valid description of the early Universe, but density perturbations are known to exist; regardless of their origin, dissipation of these perturbations through photon diffusion (Silk damping) in the early Universe will distort the CMB spectrum at observable levels [61–65]. The signal can be accurately calculated using simple linear physics and depends on the amplitude of primordial perturbations at scales with $k \approx 1 - 10^4$ Mpc$^{-1}$, some ten e-folds further than what can be probed by CMB anisotropies (Fig. 2). If the near scale-invariance of the power spectrum observed on large scales persists to these much smaller scales, then the predicted distortion, $\mu \approx (2.3 \pm 0.14) \times 10^{-8}$ [37, 64, 66], could be observed using current technology (§IV). Detecting this signal extends our grasp on primordial density

perturbations by over three orders of magnitude in scale, covering epochs that cannot be probed directly in any other way. A non-detection at this level would be a serious challenge for $\Lambda$CDM, immediately requiring new physics.

Measurements of $\mu$-distortions are directly sensitive to the power spectrum amplitude and its scale-dependence around $k \approx 10^3$ Mpc$^{-1}$ [15, 68–70]. Within the slow-roll paradigm, this provides a handle on higher-order slow-roll parameters (i.e., running of the tilt), benefitting from a vastly extended lever arm [71–73]. Outside of standard slow-roll inflation, large departures

from scale-invariance are well-motivated and often produce excess small-scale power (e.g., features [74–77] or inflection points [78–83] in the potential, particle production [84–88], waterfall transitions [89–93], axion inflation [94–96], etc. [97]), implying the presence of new physical scales that can be probed with spectral distortions (Fig. 2). In this respect, spectral distortions could establish a link to a possible primordial origin of the small-scale structure crisis [98, 99]. They could also place limits on primordial black holes [100–102], testing their role in super-massive black-hole formation [103] and as DM candidate [91, 104], the latter seeing renewed interest after the first LIGO/Virgo merger events [105–107]. Spectral distortions are also created by the dissipation of small scale tensor perturbations [108, 109] and depend on the perturbation-type (i.e., adiabatic vs. iso-curvature) [110–113], providing ways to test inflation scenarios in uncharted territory. Spectral distortion anisotropies furthermore probe local-type primordial non-Gaussianity at small scales [29, 30, 114–121], an exciting direction that complements other probes and could shed light on multi-field inflation scenarios [122].

Dark matter is another example of how spectral distortions probe new physics. Non-baryonic matter constitutes $\approx 25\%$ of the energy density of the Universe, but its nature remains unknown.

<figure><img src="image_3.png" /><figcaption>**FIG. 2:** Forecast constraints (95 % c.l.) on the primordial power spectrum for features with a $k^4$ profile that cuts off sharply at some$^{ii}$ $k_p$ [see 67, for more details]. $\mu$-distortions constrain perturbations at scales and levels inaccessible to other probes.</figcaption></figure>
The long-favored WIMP-scenario is under increasing pressure [123–128], and emphasis is gradually shifting focus towards alternatives, prominent examples being axions, sterile neutrinos, sub-GeV DM or primordial black holes [100, 129–134]. To solve this puzzle, a multi-tracer approach that combines different particle physics and cosmological probes is needed. Measurements of the CMB anisotropies themselves have clearly helped to establish the presence of DM on cosmological scales and provided tight constraints on DM annihilation and decay [135–143] and DM-SM-interactions [144–149]. However, for DM annihilation and decay CMB anisotropies quickly lose constraining power before recombination ($z \gtrsim 10^3$), being impeded by cosmic variance. Similarly, measurements of light-element abundances [135, 150–152], which are only sensitive to non-thermal energy release above nuclear dissociation thresholds in the pre-recombination era [15, 153], saturated their limits due to astrophysical uncertainties. *This is where CMB spectral distortions offer a valuable complementary probe.* For decaying particle scenarios, distortions are sensitive to particles with lifetimes $t \approx 10^6 - 10^{12}$ s [11, 15, 154–158], providing direct measurement of particle lifetimes via r-type distortions [14, 15]. Similarly, annihilating particles can be constrained using distortions; $\mu$-distortions are sensitive to light particles ($m \lesssim 100$ keV) and complement $\gamma$-ray searches for heavier particles [14, 159]. The rich spectral information added by various non-thermal processes [16, 20–22, 24, 25] will allow us to glean even more information about the nature of dark matter. Significant theoretical work is required, although it is already clear that in addition to the aforementioned examples distortions can meaningfully probe scenarios involving axions [160–162], gravitino decays [155, 163], strings [164, 165], DM-SM-interactions [141, 166, 167], macros [168] and primordial magnetic fields [169–172].

### III. PRECISION TESTS OF ACDM AND THE STANDARD MODEL

Spectral distortions also enable new tests of the standard cosmological model. The cosmological recombination and reionization eras as well as the cosmic dark ages mark important transitions in the evolution of our Universe. The largest all-sky distortion signal is indeed caused by the reionization and structure-formation processes [26, 173–177]. Energy output from the first stars and shocks heats the baryons and electrons, which then up-scatter CMB photons to create a $\gamma$-type distortion. The overall distortion is expected to reach $y \approx \text{few} \times 10^{-6}$ [26, 176, 178, 179], only one order of magnitude below the current upper limit placed by COBE/FIRAS. Such a distortion *must* exist and provides a measurement of the total thermal energy in (ionized) baryons in the Universe. A large part of the signal is due to halos with masses $M \approx 10^{13} M_{\odot}$ containing gas with an electron temperature of $kT_e \approx 2$ keV. This causes a relativistic temperature correction [180–184] to the $\gamma$-distortion that can directly tell us about feedback mechanisms [179]. The low-redshift $\gamma$-distortion from reionization is furthermore anisotropic [e.g., 26–28] and thus opens new opportunities for cross-correlation studies (e.g., with CMB and 21 cm tomography).

The cosmological recombination process causes another small but inevitable distortion of the CMB. Line emission from hydrogen and helium injects photons into the CMB, which after red-shifting from $z \approx 10^3$ is visible today as complex frequency structure in the microwave bands (Fig. 1) [17, 185–192]. The cosmological recombination radiation (CRR) has a simple dependence on cosmological parameters and the dynamics of recombination; since it includes not only hydrogen but also two helium recombinations, it probes eras well beyond the last-scattering surface observed by CMB anisotropies [18, 19, 193]. Cosmological recombination is furthermore crucial for understanding and interpreting the CMB temperature and polarization anisotropies [194–197]. It is thus critical to test our physical assumptions during this era [198–201]. *The CRR provides one of the most direct methods to achieve this.* The CRR also enables a pristine measurement of the primordial helium abundance, long before the first stars have formed. It would thus break cosmological parameter degeneracies, e.g., between the primordial helium abundance and neutrino
number [19]. Finally, interactions of CMB photons with atoms can imprint additional frequency-dependent signals through resonance [202–209] and Rayleigh scattering effects [210, 211], both of which provide independent ways for learning about recombination, the dark ages and reionization.

#### IV. THE PATH FORWARD WITH CMB SPECTRAL DISTORTIONS

The seminal measurements of the CMB blackbody spectrum by COBE/FIRAS in the early '90s cemented the Hot Big Bang model by ruling out any energy release greater than $\Delta U/U \approx 10^{-5}$ of the energy in CMB photons [4, 5, 212]. Advances since then, in both detector technology and cryogenics, could improve this sensitivity by four orders of magnitude or more (e.g., with experimental concepts like PIXIE [213, 214] or PRISM [33]), opening an enormous discovery space for both predicted distortion signals and those caused by new physics.

COBE/FIRAS was not background limited; its sensitivity was set instead by phonon noise from the 1.4 K detector. Modern detectors, operating at $\approx 0.1$ K, would have detector (dark) noise well

below the intrinsic limit set by phonon arrival statistics. The sensitivity of a background-limited instrument could be further improved by increasing the instrument's collecting area.

Figure 3 compares several predicted spectral distortions [e.g., 37] and the largest astrophysical foregrounds$^{iii}$ to the sensitivity of possible next-generation spectrometers. Pioneering steps towards $y \approx 10^{-7}$, yielding a clear detection of the expected average distortion caused by groups and clusters (see Sect. III), are possible from the ground and balloons (e.g., using concepts similar to COSMO, OLIMPO [215, 216] and ARCADE [217, 218]). However, because the distortions peak at frequencies above 200 GHz, broad frequency

coverage outside the atmospheric windows ultimately requires a space mission to detect $\mu \approx 10^{-8}$ or the CRR [219–224]. Both the anticipated signal levels (in the range 1–100 Jy sr$^{-1}$) and level of foreground cleaning are comparable to those encountered for next-generation CMB polarization measurements [e.g., 225]. Therefore, much of the technology and analysis techniques are directly transferable, although a new synergistic approach (combining multiple data sets) and observing strategy (e.g., small-patch vs. all-sky) have yet to be developed.

To conclude, CMB spectral distortions probe many processes throughout the history of the Universe. Precision spectroscopy, possible with existing technology, would provide key tests for processes expected within the CSM and open an enormous discovery space for new physics. This offers unique scientific opportunities for furthering our understanding of inflation, recombination, reionization and particle physics. Many experimental and theoretical challenges have to be overcome before we can fully exploit this new window to early- and late-universe physics. However, the potential gains are immense and the field is entering a phase of accelerated growth after decades of dormancy. With a coordinated approach, the next decade could thus see new precision measurements of one of the fundamental observables of our Universe$^{iv}$.

<figure><img src="image_4.png" /><figcaption>**FIG. 3:** Spectral distortions are observable using current technology. The signal amplitudes and required foreground cleaning are comparable to planned B-mode searches.</figcaption></figure>
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## Notes

<footnote>iWhen referring to the cosmological standard model (CSM) we assume the ΛCDM parameterization, supplemented by the Standard Model of particle physics, admitting that the presence of dark matter and dark energy requires physics beyond the latter.</footnote>

<footnote>iiTo avoid the unrealistic GW spectrum generated by a δ-function scalar power spectrum, we plot all integrated constraints using a $k^4$ spectrum – see [67] for the reason for this choice. The peak sensitivity for μ-distortions is effectively unchanged were we to instead plot constraints for δ-function features in the power spectrum with the same integrated power (see Fig. 9 therein), and also [226].</footnote>

<footnote>iiiAt high frequencies, these are dominated by dust from the galaxy and the cosmic infrared background, while at low frequencies it is synchrotron and free-free emission.</footnote>

<footnote>ivWe wish to acknowledge the generosity and support of the CERN Theoretical Physics Department in hosting the workshop "Probing fundamental physics with CMB spectral distortions" from Mar 12–16 2018 where this white paper was first conceived. This work has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (grant agreement No 725456, CMBSPEC). JC is supported by the Royal Society as a Royal Society University Research Fellow at the University of Manchester, UK.</footnote>