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FORMULA Since both Planck and ALMA are compared to the 93 GHz ACT data, small errors in the latter cancel to some degree. Employing entirely different Planck and ACT catalogs produces results in acceptable agreement with those found in Eq. REF, though somewhat larger.

2102.05079

MISSION, MISSION

Assuming the Planck-18 cosmology [CIT], we can furthermore translate the calibrated $\fsig$ to its linear value $\fsiglin$, by multiplying $\fsig$ with the ratio of the linear and nonlinear matter density fluctuation amplitudes, $\siglin / \sig = 0.905$, where $\sig$ has been computed from the adopted Cosmic Emu power spectrum. The result is also given in REF.

2102.07291

MISSION

The other origin of large numbers is Planck density: $\rho_P=5\cdot10^{96}$kg/m$^3$. Straightforward estimation for the Planck density core of only $R=1$mm radius gives the mass $M=(4/3)\pi R^3\rho_P=2\cdot10^{88}$kg, gravitational radius $R_s = 2GM/c^2= 3\cdot10^{61}$m, much larger than the mass and the radius of the observable universe $M_{uni} = 10^{53}$kg, $R_{uni} = 4\cdot10^{26}$m. Such a core will immediately cover the universe by its gravitational radius, with a large margin. To place such objects in our universe, a mechanism for mass compensation is necessary. For instance, the one of this paper, effectively negative masses created by quantum gravity and coated by positive mass shells until the equilibrium with a moderate mass value is reached.

2102.07769

UNITS, UNITS

Cosmic rays (CRs) have critical impacts in the multiphase interstellar medium (ISM), driving dynamical motions in low-density plasma and modifying the ionization state, temperature, and chemical composition of higher-density atomic and molecular gas. We present a study of CR propagation between the ionized ISM and a neutral cloud. Using one-dimensional magnetohydrodynamic particle-in-cell simulations which include ion-neutral drag to damp Alfv$\acute{\text{e}}$n waves in the cloud, we self-consistently evolve the kinetic physics of CRs and fluid dynamics of the multiphase gas. By introducing the cloud in our periodic domain, our simulations break translational symmetry and allow the emergence of spatial structure in the CR distribution function. A negative spatial gradient forms across the fully-ionized ISM region while a positive gradient forms across the neutral cloud. We connect our results with CR hydrodynamics formulations by computing the wave-particle scattering rates as predicted by quasilinear, fluid, and Fokker-Planck theory. For momenta where the mean free path is short relative to the box size, we find excellent agreement among all scattering rates. By exploring different cloud sizes and ion-neutral collision rates, we show that our results are robust. Our work provides a first-principles verification of CR hydrodynamics when particles stream down their pressure gradient, and opens a pathway toward comprehensive calibrations of transport coefficients from self-generated Alfv$\acute{\text{e}}$n wave scattering with CRs.

2102.11877

FOKKER

In this work we realised the scotogenic model through $A_{4}\times Z_{4}$ discrete flavor symmetry. The implications of the discrete symmetry can be seen as it contraints the Yukawa couplings of a particular model. Here, we produce a realistic neutrino mixing to do an extensive analysis of lepton flavor violating processes. Considering different lepton flavor violating(LFV) proceses such as $l_{\alpha}\rightarrow l_{\beta}\gamma$ and $l_{\alpha}\rightarrow 3l_{\beta}$, we analysed their impact on the neutrino phenomenology as well. The most stringent bounds on LFV comes from the MEG experiment [CIT]. The limit on branching ratio for the decay of $\mu \rightarrow e\gamma$ from this experiment is obtained to be Br($\mu \rightarrow e\gamma$)$< 4.2\times 10^{-13}$. In case of $l_{\alpha}\rightarrow 3 l_{\beta}$ decay contraints comes from SINDRUM experiment [CIT] is set to be $\rm BR(l_{\alpha} \rightarrow 3l_{\beta})<10^{-12}$. Neutrinoless double beta decay($0\nu\beta\beta$) is also studied within the model by the consideration of the constraints from KamLAND-Zen experiment. We have also incorporated BAU within the model and have shown the viable parameter space satisfying the Planck bound.

2103.05295

MISSION

In the compactifications considered here, the number of axions resulting from the Ramond-Ramond four-form $C_4$ is the Hodge number $h^{1,1}_+$ of the orientifold [CIT], which we write as $h^{1,1}$ for notational simplicity. Upon including the scalar potential generated by instantons, the effective Lagrangian for the axion fields $\theta^i$, $i=1,\ldots, h^{1,1}$ takes the form FORMULA where $M_{\mathrm{pl}}$ is the reduced Planck mass, $K_{ij}$ is the Kähler metric, $g^{\mu\nu}$ is the inverse of the spacetime metric, $\Lambda_a$ is a mass scale associated to the $a$th instanton, $\mathcal{Q}^{a}_{i} \in \mathbb{Z}$ is the charge of the $a$th instanton under the $i$th axion shift symmetry, and $\delta^a$ is a $CP$ phase.

2103.06812

UNITS

In the tetron model the situation is much simpler. As discussed before, the Planck energy $E_0 \sim E_s$ contained in the neighborhood volume $L_0^3$ of one bound constituent is the binding energy of tetrons in an empty flat spacetime and does not affect the curvature(=accelerated expansion), because it is a constant contribution in the conservation of energy law (REF). Furthermore, quantum fluctuations do not exist by themselves at any point in the universe, but are an artefact of the discreteness of the universe [CIT] and exist only where a matter field is gliding as quasiparticle excitation on the discrete tetron background.

2103.09622

UNITS

From we see that travel time fluctuations would exceed this $\order{\rm{ms}}$ scale for $\gtrsim$GeV particles in the 'natural' scenario shown when the energy suppression is $E / M_{\rm{Planck}}$ ($n=1$), which has enabled Planck scale limits on velocity fluctuations to be set using $\order{\rm{GeV}}$ $\gamma$-rays from this GRB [CIT]. Should $\gtrsim$TeV neutrino emission be eventually detected from distant GRBs, we see that the sensitivity to Planck scale physics will significantly exceed that currently available from GeV photon observations, allowing the possible detection of quantum gravity effects beyond the reach of current measurements (for example if the energy scale of quantum gravity exceeds $M_{\rm{Planck}}$, or $\delta L_{0}< \delta L_{\rm{Planck}}$). In fact, even longer duration sources (seconds or minutes) could still yield Planck scale physics signals for $>$TeV particles. Combined analyses of neutrino emission from multiple GRBs and multiple neutrino telescopes could be used to help overcome the low statistics inherent in neutrino point source observations when compared to $\gamma$-rays.

2103.15313

UNITS, UNITS, UNITS, UNITS, UNITS, UNITS

Fig. REF compares $\sigma_8$ constraints from our high-$z$ study with those from low-$z$ studies in the literature. Our constraint on $f\sigma_8(z)$ is derived by converting our constraints on $(\Omega_{{\rm m}0}, \sigma_8)$ into $f\sigma_8(z)$, where $f=-{\rm d} \ln D(z)/{\rm d} (1+z)$ is the logarithmic growth rate and $\sigma_8(z)=\sigma_8D(z)/D(0)$ is the linear matter fluctuation at redshift $z$. Our constraints on both $\sigma_8$ and $f\sigma_8(z)$ are roughly consistent with constraints computed from the Planck 2018 TT,TE,EE+lowE+lensing result [CIT], while our constraints are lower than the Planck cosmology at the $1.4\sigma$ level for both $\sigma_8$ and $f\sigma_8(z)$. Motivated by the potential deviations from the Planck constraints on $\Lambda$CDM cosmology we repeat the same analysis with the assumption that the time dependent dark energy is characterized by the equation-of-state parameter $w(a)=w_0+(1-a)w_a$. We find that again our constraint is consistent with the Planck cosmology.

2103.15862

MISSION, MISSION, MISSION, MISSION

The calculation utilized the following equation [CIT] to compute the mass of each continuum source [see also equation 1 in [CIT]]: FORMULA where $F_\nu$ is the total integrated flux (in Jy), $D$ is the distance (in kpc), $R_t$ is the gas-to-dust mass ratio, $B_\nu$ is the Planck function for a dust temperature $T_D$, and $\kappa_\nu$ is the dust absorption coefficient. In this calculation, we considered $\kappa_\nu$ = 1.85,cm$^2$,g$^{-1}$ at 870 $\mu$m [CIT], $R_t$ = 100, and $D$ = 5.7 kpc.

2104.03627

LAW

In figure 4 we present the reconstruction of the Hubble parameter using the $GaPP$ code. In the top we present the model-independent reconstruction of $H (z)$, where we have used the $CC + BAO$ data to determine the Hubble constant ($H_{0} = 69.45 \pm 4.34$). In the other two figures we reconstructed $H(z)$ using as prior for the Hubble constant the values of the Planck and SH0ES Collaborations. In all cases, the reconstruction is done with $1\sigma$ of uncertainty. In figure 5 we can observe the reconstruction of the cosmographic functions $q (z)$, $j (z)$ and $s (z)$ without using a prior value for the Hubble constant. In particular the deceleration parameter shows that the transition redshift, $z_{tr}$, from a decelerated universe to an accelerated universe, defined as $q(z_{tr})=0$, is into the region $z <1$ with $2\sigma$.

2104.07356

MISSION

In the case of nonminimal coupling slow roll occurs when the scalar field rolls down from the local maximum of the potential at the fixed point $B_\pm$ towards the central fixed point $A$. For instance, taking the point $B_-$ on Fig. REF, only those solutions can experience enough inflation which either cross over the potential maximum from the left at sufficiently low "speed" z, or which climb up towards the potential maximum from the right but do not shoot over the top. Both options have a rather limited range and thus the band of good initial conditions narrows down compared to the minimally coupled case. The situation becomes even more precarious at high nonminimal coupling $\xi$, because the fixed points are pushed closer to the center and the path of the possible slow roll gets shorter. Only very finely tuned initial conditions whereby the field evolution is really slow near the maximum of the potential, grant the privilege to experience at least 50 e-folds of accelerated expansion. Thus for quadratic potentials invoking nonminimal coupling severely limits the range of initial conditions conductive for proper inflation. Let us remark, that in the nonminimal coupling case there are also extreme kinetic solutions near the boundary of the physical phase space which cross over $\phi=0$ (too narrow to be shown explicitly). Among these there are some lucky trajectories which slow down precisely enough to reach the vicinity of $B_\pm$ and subsequently partake in the inflationary regime. The immediate assessment of the physicality of the initial conditions requires now extra caution, however, since the effective Planck mass is dynamical in the nonminimal coupling case. Due to the resulting ambiguity in delimiting the region of Planckian energy density, we have instead opted to delineate all trajectories which give sufficient inflation.

2104.10183

UNITS

For stars closer than 300 pc, the offset angle is $\theta_\mathrm{star} - \theta_\mathrm{Planck} = -71^\circ \pm 45^\circ$ and shows large variation, while for stars farther than 300 pc, the offset angle is $\theta_\mathrm{star} - \theta_\mathrm{Planck} = 2^\circ \pm 28^\circ$. $\theta_\mathrm{Planck}$ traces the *B*-field approximately in proportion to the column density along the LOS. Thus, $\theta_\mathrm{Planck}$ mainly traces the Perseus molecular cloud, with an additional contribution from the foreground cloud (see Figure REF). As discussed in Section [3.4], this also applies to $\theta_\mathrm{star}$ of Group 1. As a result, $\theta_\mathrm{Planck}$ agrees well with the Group 1 $\theta_\mathrm{star}$ as they trace the similar ISM on the LOS. On the other hand, $\theta_\mathrm{star}$ of Group 2 and Group 3 has no contribution from the Perseus cloud, and the foreground contribution traced by them is much smaller than that of the Perseus cloud in the background. Therefore, $\theta_\mathrm{star}$ of Group 2 and Group 3 does not correlate with $\theta_\mathrm{Planck}$. Thus, we conclude that $\theta_\mathrm{star}$ and $\theta_\mathrm{Planck}$ observations of the Perseus molecular cloud's direction with stellar distances $d > 300$ pc are in good agreement with each other, despite the fact that their spatial resolutions are largely different from each other. The spatial resolution of $\theta_\mathrm{Planck}$ is $10'$, which corresponds to $\sim 1$ pc at 300 pc from the sun. On the other hand, the spatial resolution of $\theta_\mathrm{star}$ is the size of stellar photospheres, which is much smaller than the Planck's beam size.

2104.11932

MISSION, MISSION, MISSION, MISSION, MISSION, MISSION, MISSION, MISSION, MISSION

In order to constrain the aforementioned models (and their respective parameters), we use the public Planck likelihood code and associated data sets[^2], namely the latest 2018 release containing the final temperature and polarisation (both E and B modes) measurements from the satellite [CIT]. We consider both the low- and high-multipole ($\ell$) data as well as the likelihood associated to the lensing convergence map extracted from the same measurements [CIT]. Additionally, as an alternative to the Planck low-multipole B-mode polarisation data, we also consider the joint BICEP2/Keck-WMAP-Planck likelihood of [CIT], which provides significantly more stringent constraints and should noticeably affect our results. Three data set combinations are considered thereafter:

2104.15091

MISSION, MISSION, MISSION

We thank David Weinberg and Matias Zaldarriaga for insightful comments on earlier versions of this work. We thank Yuto Minami and Eiichiro Komatsu for sharing the sky masks used in their analysis. S.E.C. acknowledges support by the Friends of the Institute for Advanced Study Membership. C.-G.K. and B.S.H. acknowledge support from the NASA TCAN grant No. NNH17ZDA001N-TCAN. J.C.H. thanks the Simons Foundation for support. This work makes use of observations obtained with Planck (http://www.esa.int/Planck), an ESA science mission with instruments and contributions directly funded by ESA Member States, NASA, and Canada. Hi4PI is based on observations with the 100-m telescope of the MPIfR (Max-Planck- Institut für Radioastronomie) at Effelsberg and the Parkes Radio Telescope, which is part of the Australia Telescope and is funded by the Commonwealth of Australia for operation as a National Facility managed by CSIRO. This research has made use of NASA's Astrophysics Data System.

2105.00120

MISSION, MISSION, MPS

In order to check the validity of the geometry that the L-component in region 3 is located behind the LMC disk, we compare the dust extinction with the dust emission; the dust extinction is caused by only the dust in front of the stars while the emission can come from all dust. As a dust emission map, we use the map of the dust optical depth at 353 GHz, $\tau_{353}$, obtained from the Planck and IRAS far-infrared data ([CIT]). To estimate $\tau_{353}$ in the LMC, [CIT] calculated the Galactic foreground dust optical depth from the foreground H, intensity ($W$(H,)) using the conversion factor from $W$(H,) to $\tau_{353}$ derived from [CIT]. We use the $\tau_{353}$ map after subtraction of the foreground component.

2105.05421

MISSION

Sidney Coleman has said that the symmetry of vacuum is the symmetry of the world. In Quantum Field Theory, one may have a vacuum devoid of particles but still containing meaning. So we need to investigate the symmetry of the vacuum. The vacuum has meaning because of Hawking radiation, which in turn is based upon the Heisenberg uncertainty principle. It turns out that energy need not be conserved in physics for tiny times, $\Delta E \le \hbar /\Delta t$, where $\hbar$ is a fundamental constant of nature (over a $2 \pi$) named after Planck. The physical picture is this: for small times, a fermion pair, such as electron and positron, may pop out of the vacuum and maintain vacuum quantum numbers as long as it subsequently pops back into the vacuum. The particles are said to be virtual in that they are not observed. In fact, neutrinos are never observed, and therefore always virtual.

2105.07502

PERSON

Numerous efforts have been made to identify possible errors in the respective data analysis processes of each set of probes. Concerning the local measurements of the Hubble parameter, examples of these efforts can be found in the most recent review of the distance ladder [CIT]. Large-scale structure surveys have also carried out extensive systematics checks and internal consistency tests; see [CIT] for the Dark Energy Survey, [CIT] for the Kilo-Degree Survey (KiDS), and [CIT] for the Baryon Oscillation Spectroscopic Survey (BOSS) and the Extented Baryon Oscillation Spectroscopic Survey (eBOSS) respectively. As for the CMB probes, [CIT] undertook a thorough revision of the CamSpec Likelihood used to analyse Planck data in search of potential sytematics. Moreover, the initiative 'Beyond Planck' is currently conducting a thorough revision of the Planck and WMAP methodology [CIT].

2105.09545

MISSION, MISSION, MISSION

In order to validate our analysis pipeline, we have verified that the constraints on $\Lambda$CDM from our data agree well with those found by the different collaborations. Doing so has also allowed us to explore the constraints our full complement of data sets is able to place on this model when combined, measuring the $S_8$ parameter to be $S_8=0.7781\pm 0.0094$. This is in good agreement with current constraints from other groups, and in tension with Planck at the $\sim3.4\sigma$ level. This also shows that, in combination, current large-scale structure data are able to constrain these parameters with an uncertainty that is significantly ($\sim25\%$) better than that achieved by primary CMB data.

2105.12108

MISSION

We apply the pipelines developed for the E2E Planck simulations to the ` SMICA` temperature map. We divide the full (except for the mask) sky Planck map into smaller patches, as was done for the simulations, and compare the histogram of predictions for both pipelines with the histograms of the individual $G\mu$ classes from simulations through calculating the *P*-value for each case. The measured *P*-values for all cases are below $0.0027$ which corresponds to the $3\sigma$ frequentist level. We therefore conclude that $G\mu$ is below the minimum detectability limit of the network with $3\sigma$ significance. The $3\sigma$ upper bound on the $G\mu$ as estimated from Planck sky is $G\mu \lesssim 8.6 \times 10^{-7}$, for both LightGBM and deep search methods.

2106.00059

MISSION, MISSION, MISSION

This equation is an alternative form of Eq. (REF), convenient for the formal reduction to the off-shell Fokker-Planck equation. For this purpose we exploit the separation of scales between the meson masses, as the mass of the $D$ meson is much larger than the temperature, and any of the light-meson masses. Such a Brownian picture implies that the typical momentum exchanged in the elastic collision is of the order of $T$ and much smaller than the total momentum of the heavy particle ${\bf q} \ll {\bf k}$ [CIT].

2106.01156

FOKKER

Actually, the Thomson optical depth measured by Planck, $\tau=0.0544\pm 0.0073$ [CIT], can also be well reproduced by our SF model under reasonable assumptions for the escape fractions of ionizing photons. Fig. REF shows the evolution of $\tau$ with redshift predicted by our merger trees, which agrees well with the Planck result assuming escape fractions $f_{\rm esc,II}=0.1$ for Pop I/II and $f_{\rm esc,III}\sim 0.1-0.3$ for Pop III. With these escape fractions, the predicted volume filling fraction of ionized gas reaches $\simeq 1 (0.5)$ at $z\simeq 5.5 (8)$, consistent with the picture of late reionization. The escape fractions adopted here are within the typical range $f_{\rm esc}\sim 0.1-0.7$ seen in simulations and semi-analytical models (e.g. [CIT]).

2106.02244

MISSION, MISSION

The concept of cosmic inflation has been extremely effective in explaining different properties of the early universe [CIT]. Various satellite observations have consistently confirmed inflationary estimates for the early universe, and the most recent evidence from the Planck experiment continues this trend [CIT]. Furthermore observational evidence supports a wide range of inflationary models, a lot of which are inspired by radically different contexts ranging from modified gravity theories to quantum gravitational [CIT]. However, traditional single field models (which some refer to as \"supercooled inflationary models [CIT] \") have a lot of empirical support and are still widely used in theoretical studies.

2106.03578

MISSION

To characterise how the energy density in GWs is distributed over frequencies today we introduce the gravitational wave power spectrum [CIT] FORMULA where $f$ is frequency and $d\rho_{\text{gw}}$ is the gravitational wave energy density within a frequency interval $df$. The critical density is $\rho_{\text{c}} = {3H^2}/{8\pi G}$, where $H$ is the Hubble rate, $G$ is the gravitational constant and $c$ is the speed of light. Quantities evaluated at the present day are given the subscript 0. For the Hubble constant $H_0$ we take the central value measured by the Planck satellite $H_0= 67.4, \text{km s}^{-1}\text{Mpc}^{-1}$ as given in [CIT].

2106.05984

MISSION

Let us check what conditions are imposed by FL on this scenario, where the radion has been stabilized by the combined effect of Casimir and $(d+1)$-dimensional vacuum energies to some value $\phi_{\text{min}}$. In $d$ dimensions, we can apply the FL inequality to the Kaluza-Klein $U(1)$ so that (REF) becomes a bound on the mass of KK modes. The gauge coupling is[^9] (REF) evaluated at $\phi_{\text{min}}$. Since the dilaton has been stabilized, we can ignore the first condition in (REF) and directly apply the bound on the spectrum of massive states. For a mode with KK charge $q$, this becomes FORMULA In particular, we may apply this to the Kaluza-Klein modes of the $(d+1)$-dimensional graviton itself, which are always present and have masses (in $d$-dimensional Planck units) FORMULA Combining with (REF), and setting $q=1$, we obtain a bound relating the stabilized value of the radion field and the vacuum energy $e^{-\gamma\phi}\gtrsim V$. This can be rewritten purely in terms of the physical KK scale in $d$-dimensional Planck units, as FORMULA Equation (REF) is the main result of this Section. It says that the cut-off of the $d$-dimensional field theory must be above the $d$-dimensional Hubble scale. One could worry that this is just a self-consistency condition of the FL picture, or even of dimensional reduction; but the computation based on the Schwinger effect works even when there is a whole tower of light particles, one just needs to consider the tower version of the conjecture we outlined in Section [2.2.1][^10]. We also note that the interesting case of $d+1=4$ must be excluded from the discussion since there are no charged Nariai black holes in three dimensions. With this caveat, we conclude that (REF) is a constraint that should be imposed for consistency of a KK vacuum with positive vacuum energy, and that FL provides a modest lower bound on the size of the extra dimensions.

2106.07650

UNITS, UNITS

The simulated sample might not contain any steep spectrum sources for several reasons. The simulations might fail to reproduce such sources, because we did not model the energy gains and losses of the accelerated electrons, e.g. using a Fokker-Planck solver [e.g. [CIT]]. Furthermore when compiling the simulated sample, we only included bright radio relics. In order to produce such bright relics in simulations, strong shock waves are needed. This bias could be overcome, if one includes the effect of re-acceleration in the simulations. An other cause could be that we did not mimic any of the observational challenges, such as detection limits or exposure time, when computing the radio spectra. On the other hand, it is also possible that the observations are underestimating the spectral indices. For the majority of relics, the observed spectrum was measured at three frequencies. If one of these measurements is shallow, improperly deconvolved, or performed without any matching uv-coverages, the observed spectrum might appear steeper. Recent observations by [CIT] highlighted the importance of enough frequency coverage, when computing integrated radio spectra. In addition, proper subtraction of unrelated sources is very important which may also steepen the spectrum. However, to fully understand the differences between the observed and simulated radio Mach numbers, more and deeper observations as well as more sophisticated simulations, that carefully follow the spectral evolution of the cosmic-ray electrons, are required.

2106.08351

FOKKER

The entanglement entropy captures the quantum entanglement in a pure state between $A$ and $B$ for a bipartite system $A\cup B$. The study of entanglement entropy has played an essential role in our understanding of the emergence of spacetime and holography. These progresses begin with the Ryu-Takayanagi (RT) proposal [CIT] that reveals the deep connection between the spacetime geometry and quantum entanglement. In AdS/CFT [CIT], consider a static region $A$ in the boundary field theory and the minimal surface $\mathcal{E}_{A}$ that is in the dual AdS bulk and anchored to $\partial A$, the RT formula relates the entanglement entropy of $A$ to the area of $\mathcal{E}_{A}$ in Planck units, i.e. FORMULA This relation between the quantum entanglement and geometry has recently been extended to holographic theories beyond AdS/CFT, for example the (warped) AdS/(warped) CFT correspondence [CIT] and 3-dimensional flat holography [CIT], whose dual field theory is non-Lorentz invariant. These new relations are derived firstly via the Rindler method [CIT], which constructs a Rindler transformation that maps the entanglement wedge to a Rindler spacetime with infinitely far away boundaries, then calculates the entanglement entropy via the thermal entropy in the Rindler spacetime. Later they are also derived in [CIT] via the Lewkowycz-Maldacena prescription [CIT], which directly applies the replica trick in the bulk to calculate the entanglement entropy. However, in these cases, there exists a subtle issue about the cut-off in the bulk causing the RT surfaces not anchored on the boundary[^1]. This issue can be solved at least in 2+1 dimensions by introducing certain null geodesics emanating from the boundary of $A$. Indeed the analogue of the RT surface $\mathcal{E}_{A}$ is the extremal geodesic whose length is at the saddle among all the geodesics that anchored on the null geodesics, then the holographic entanglement entropy is given by the length of the extremal geodesic.

2106.12397

UNITS

All data is then regridded onto a 3$\arcsec$ pixel size grid. We use a Gaussian derivative kernel to calculate the gradient ($\nabla N$). For the column density maps to be compared with the HAWC`+`polarization angle, we chose a kernel with a FWHM of $12 \arcsec$. For the column density maps to be compared with the Planck polarization angle, we chose a kernel with a FWHM of $30 \arcsec$. These kernel sizes are chosen such that they are large enough to smooth out and remove any potential edge or corner effects that may create erroneous gradient vectors, and yet small enough such that no significant degradation of the resolution of our gradient map occurs.

2106.13795

MISSION

Our observations were carried out between 18 and 19 April 2018, program ID 0101.B-0560(A) (PI Iglesias-Groth) using the bolometer LABOCA on APEX [CIT]. We observed in mostly excellent weather conditions (PWV 0.5 mm and 0.9 mm). The data were reduced using the CRUSH [^4] package, which is a free data reduction software for specific astronomical imaging arrays. It is especially designed for use with ground-based or air-borne (sub)millimeter wave cameras. Individual maps were co-added (noise-weighted) and the final map was beam smoothed, resulting in a spatial resolution with full width at half maximum (FWHM) of 19.5 arcsec. The total source observing time of the used data for this analysis is 8400 seconds and the average rms across the field is $8$ mJy beam$^{-1}$. A submillimeter source is detected with coordinates consistent with those of *WISE* J022057.56-383311.4 which is partially responsible of the observed Planck submillimeter fluxes. We measure a APEX/LABOCA flux of $S_{870\mu m}= 54 \pm 8$ mJy. The differences with the expected Planck measurements (see Fig. REF) are due to the flux of the Sunyaev-Zeldovich ($SZ$) effect of a near galaxy cluster PSZ2 G249.80-68.11, at 4.5 arcmin north from our source at $z=0.228$ [CIT]. In fact, the position of the source coincides with the arc structures of the strong lensed galaxy seen in the *HST* images as can be seen in Figure REF(a). In Figure REF(a) we see the flux detection at S/N$\sim 6.6$.

2106.14281

MISSION, MISSION

The PSM, as implemented in the Planck full sky simulations [CIT], is also publicly-available in the form of the "full focal plane" simulations on the Planck Legacy Archive.[^7] While the GSM simulates the total diffuse sky emission present at each frequency, the PSM provides separate component maps for (e.g.) free-free and synchrotron emission. We assemble a set of foreground maps from the PSM using the method detailed in [CIT]. The pertinent details of our PSM model are summarised in Table REF, and the individual components are shown in Fig. REF.

2107.02267

MISSION, MISSION

We present a static and axisymmetric traversable wormhole spacetime with vanishing Arnowitt-Deser-Misner (ADM) mass which is characterized by a length parameter $l$ and a deformation parameter $a$ and reduces to the massless Kerr vacuum wormhole as $l\to 0$. The spacetime is analytic everywhere and regularizes a ring-like conical singularity of the massless Kerr wormhole by virtue of a localized exotic matter which violates the standard energy conditions only near the wormhole throat. In the spherically symmetric case ($a=0$), the areal radius of the wormhole throat is exactly $l$ and all the standard energy conditions are respected outside the proper radial distance approximately $1.60l$ from the throat. While the curvature at the throat is beyond the Planck scale if $l$ is identical to the Planck length $l_{\rm p}$, our wormhole may be a semi-classical model for $l\simeq 10l_{\rm p}$. With $l=10l_{\rm p}$, the total amount of the negative energy supporting this wormhole is only $E\simeq -26.5m_{\rm p}c^2$, which is the rest mass energy of about $-5.77\times 10^{-4}{\rm g}$. It is shown that the geodesic behavior on the equatorial plane does not qualitatively change by the localization of an exotic matter.

2107.07052

UNITS, UNITS

The 2018 release of the Planck cosmic microwave background (CMB) measurements determined that the primordial scalar perturbations are nearly scale invariant [CIT]. Its results improve the Planck 2015 consequences [CIT] in which they are more consistent with a vanishing scale dependency of the spectral index in standard model of cosmology. These measurements support the main predictions of single-field inflationary models, which supposed the universe to have undergone a brief period of extremely rapid expansion right after the big bang [CIT].

2107.08331

MISSION, MISSION

In bounce cosmology, an initial contraction phase precedes the expansion of the universe, and a big bounce basically replaces the big bang singularity. Loop quantum cosmology (LQC), which will be assumed for the high-energy regime in this article, is derived by quantizing Friedmann--Lemaître--Robertson--Walker (FLRW) spacetime using loop quantum gravity (LQG) ideas and techniques [CIT]. As the universe contracts coming to its Planck regime, when the space-time curvature gets close to the Planck scale, quantum gravity effects become considerable and lead to a connection between the contraction and expansion phases of the universe at the bounce point [CIT]. Notice that the trans-Planckian problem is also avoided because the wavelengths of the fluctuations we are interested in remain many orders of magnitude larger than the Planck length [CIT].

2107.08331

UNITS, UNITS, UNITS

[^2]: It is worth pointing out that an eV scale majoron is not unmotivated from theoretical perspective. It has been shown that a perturbative breaking of the lepton number symmetry by quantum gravity at the Planck scale is roughly consistent with generating an eV scale majoron mass (see [CIT]).

2107.10291

UNITS

As illustrated quite nicely by figure REF from the COBE satellite, at a first glance the CMB appears to be completely isotropic. This is actually one of the motivations for inflation, as in a pure radiation/matter-dominated universe the CMB would come from regions that have never been in causal contact, and so it would be very unlikely for the CMB to be this isotropic (this is called the horizon problem). Looking more closely, we see that at the level of $10^{-3}$ K there is a dipole component, caused by the movement of the Earth with respect to the Hubble flow. Finally, at the level of $10^{-5}$ K we see fluctuations in all multipoles $\ell$ (in terms of a spherical harmonic decomposition). Of course the latter are now measured at much higher resolution by the Planck satellite, see figure REF. These are the fluctuations that were presumably generated by inflation, as explained in the previous section, and that at later times formed the seeds of structure formation by gravitational collapse. Because these fluctuations are so small, perturbation theory works very well, which is one reason why the analysis of CMB data is simpler than the analysis of large-scale structure data. Linear perturbation theory is a very good approximation, but because of the high precision of current CMB data we even have access to second-order corrections, the so-called non-Gaussianities that will be at the centre of this thesis.

2107.10802

MISSION

The work in Planck was organised in so-called working groups, each of which was in charge of a specific part of the analysis, often associated with one of the main publications. For the non-Gaussianity working group, most relevant for the work in this thesis, we required several products produced by other working groups (most of which had their own prerequisites). In the first place we needed of course the cleaned CMB sky maps, produced by the component separation working group from the raw sky maps of the different frequency channels (at an effective 5 arcmin resolution). In order to compute error bars, the linear correction term (see chapter [6]), and for data validation purposes, we also required simulations. The so-called FFP (Full Focal Plane) simulations were produced several times (as indicated by different version numbers) over the course of the Planck data analysis years, including more and more effects and hence becoming more and more realistic over the years. The final version, called FFP10 and used in the 2018 data analysis, consisted of a set of CMB-only map realisations (including the effects of gravitational lensing, satellite scanning, and beam asymmetries), and a set of noise-plus-systematics realisations (of which the input also included a fixed CMB and foreground realisation, which was subtracted at the end, so that any sky-signal distortion effects are included as well). These were then passed through the component separation pipelines in the same way as the real sky map. The required beam transfer functions and confidence sky masks (for temperature and polarization) were also provided by the component separation working group. From the simulations we could determine the CMB power spectrum and noise power spectrum to be used in the estimator weights. Finally we required the values of various cosmological parameters to determine the theoretical bispectrum templates, which were provided by the power spectrum likelihood and parameters working group. Conversely, the results produced by the non-Gaussianity working group were used to test for example the quality of the component separation products. This illustrates the important interactivity between the different working groups in the Planck collaboration.

2107.10802

MISSION, MISSION, MISSION

However, in order to trust the classical description of the solutions and to neglect quantum effect that may destroy the individual microscopic bubbles, their sizes must be larger than the six-dimensional Planck volume. Hopefully, the area of individual bubbles are computable analytically REF(#eq:AreaBubbleAppcharged){reference-type="eqref" reference="eq:AreaBubbleAppcharged"}, and we must therefore impose FORMULA If we consider that $R_{y} = \lambda,\ell_P^{(4)}$ where $\lambda$ is a dimensionless factor, and use the relation between the four-dimensional and six-dimensional Planck lengths, ${\ell_P^{(6)}}^2,=, R_y,\ell_P^{(4)}$, we find that the maximum number of bubbles possible to have a trustworthy solution is FORMULA where $m^{(4)}_P$ is the four-dimensional Planck mass. More concretely, if the extra dimension is $\lambda={\cal O}(10^{14})$[^12] bigger than the four-dimensional Planck length, which is already rather large (of order $10^{-13}$ m), the maximum mass for such solutions is ${\cal O}(10^{21})$ bigger than the Planck mass (of order $10^{13}$ kg). It would be rather optimistic to state that those solutions can live in an astrophysical regime. However, one can bypass this maximal bound by allowing once again conical defects at the bubbles, that are classically resolved into Gibbons-Hawking cycles [CIT]. For instance, by imposing the same conical defect at each bubble, parametrized by an integer $k\in \mathbb{N}$, the solutions are identical with the rescaling $\widetilde{R}_{y_a} \to k,\widetilde{R}_{y_a}$, i.e. $\widetilde{R}_{y} \to k,\widetilde{R}_{y}$. Considering $k$ to be large allows to take arbitrary large mass for the Weyl stars.

2107.13551

UNITS, UNITS, UNITS, UNITS, UNITS

The structure of the Hamiltonian constraint for general relativity -- the Wheeler-DeWitt equation -- is similar both in structure and origin to the constraint of the simple model just discussed. Including the energy of a scalar matter field, the Wheeler-DeWitt equation reads FORMULA Here $T_{nn}(\Phi, \Pi)$ is the stress-energy of the matter field expressed in terms of the field's value and momentum and projected onto the normals of the spacelike hypersurface. It is the Hamiltonian density for the scalar field. The inverse squared Planck length enters the constraint in exactly the same way as the mass of the clock did in the model problem [cf. (4.15),(4.19)]. We may therefore consider the limit when $\ell \rightarrow 0$ and expect to treat geometry semiclassically [21-24]. This is the limit when relevant length scales are large compared to the Planck length and when relevant energies are small compared to the Planck mass.

2108.00494

UNITS, UNITS, UNITS

Another discrepancy may occur in the $\sigma_8$ and $\Omega_m$ relation as shown in Fig.,REF, the graphic was adapted from [CIT]. A relatively new tool in Cosmology is Cosmic shear [CIT]. Cosmic shear is created by large-scale structure in the Universe which distort images of distant galaxies due to weak gravitational lensing. Properties on large scales as well as the geometry of the Universe can be concluded by measuring galaxy shape correlations. Note, however, that in the following study a spatially flat Universe based on $\Lambda$CDM has been adopted. The so called *Cosmic shear bananas* compare the relationship between $\sigma_8$ and $\Omega_m$ as it can be seen on the left hand side of Fig.,REF and $S_8$ and the total mass density $\Omega_m$ on the right hand side. Thereby is $S_8$ defined as $S_8=\sigma_8\sqrt{\Omega_m/0.3}$ and $\sigma_8$ is the standard deviation of matter density fluctuations in spheres with a comoving radius of 8 Mpc/h. The Planck data results are shown in bright red. Depending on the redshift calibration, discrepancies up to $3\sigma$ may arise. The turquoise stars in the figure below, Fig.,REF indicate roughly the values of $\sigma_8$ and $\Omega_m$ according to the SU(2)~CMB~ fit. Their values are shown in Fig.,REF. Note that the stars in Fig.,REF are drawn in by hand and are *not* plotted and that the shear model relies on $\Lambda$CDM.

2108.02244

MISSION

We also show this result in Figure REF. Fig. REF shows the joint 1-$\sigma$ and 2$\sigma$ confidence contours for ($h, b$) from Planck, H chronometers, and Pantheon data. The darker and lighter regions represent 1-$\sigma$ and 2-$\sigma$ CL regions, respectively. The left panel of this figure corresponds to the case with the prior on the value of $\Omega_{m0}$ as $0.274$. Within $68$ % CL, the value of $b$ is above zero to indicate the deviation from CDDR. When we fix $\Omega_{m0} = 0.314$, the $68$ % and $95$ % confidence contours for ($h, b$) are shown in the right panel of Fig. REF. However, the current data is consistent with the standard model in this case even within $1$-$\sigma$ CL.

2108.06043

MISSION

We find that turning on general relativity (i.e turning on post-Newtonian corrections) causes us to lose resolution near the singularity. This is made evident by the light-grey data points, which correspond to prompt mergers of two of the particles. We also find that we lose resolution in the binary-single scattering regime. Due to the loss of resolution near the singular regions, we can no longer verify that the previously identified patterns (e.g., repeating swaths of chaos and regular regions) will continue down to the Planck Scale, assuming gravity remains classical in this limit. This loss of resolution occurs because the two black holes merge when they approach the Schwarzschild radius, which is much larger than the Planck scale.

2108.06335

UNITS, UNITS

The method is based on the computation of the level of correlation of the QUIJOTE maps $\textbf{m}_{\rm QJT}$ with the CMB anisotropies maps $\textbf{m}_{\rm CMB}$ as traced by Planck data, accounting simultaneously for the chance alignment between the CMB and the Galactic foregrounds. We assume that the QUIJOTE map of a given horn and frequency is a linear combination of the CMB map, of a template of Galactic foregrounds **f**, and of the noise **n**, as: FORMULA where $\alpha$ and $\beta$ are the parameters of the linear combination of the CMB and the foregrounds map, respectively. Let us perform a cross-correlations of the QUIJOTE map with the CMB and with the foregrounds map, which gives: FORMULA where $C_\ell^{X \times Y}$ is the cross power spectrum of map $X$ and map $Y$. In Eq. REF, we assumed that the noise map of QUIJOTE does not play any role in the cross-correlations, and that the parameters $\alpha$ and $\beta$ do not change with the angular scale. By solving this system of equations with respect to $\alpha$ we get: FORMULA where the brackets $<\cdot>$ represent an average within all multipoles in the range $\ell\in[100,200]$, so in proximity of the first peak of the CMB angular power spectrum. This range of multipoles is a particular selection in which, first, the CMB power spectrum is in the signal dominated regime with respect to the signal error of the QUIJOTE maps (as shown in Fig. REF), and second, any residual from the dipole mode coupling which is left by the power spectrum estimator is negligible (see discussion in Sec. [6.2]). If the CMB anisotropies are correctly recovered, and the QUIJOTE maps are properly calibrated, we expect to measure with Eq. REF a value of $\alpha=1$, which can be read as the amplitude of the CMB anisotropies map measured by QUIJOTE.

2108.09063

MISSION

The main point of this article is that two of these examples --- the metastability of the electroweak vacuum and the smallness of the (running) Higgs mass compared to the Planck mass --- are in fact not entirely independent, as a small Higgs mass is a necessary condition for metastability. In other words, *any* explanation of metastability also offers a path towards a solution to the Higgs naturalness problem.

2108.09315

UNITS

As ACT is highly complementary to Planck, which has a better sensitivity to anisotropies at larger scales, we also explore constraints on our feature models from their combination. In order not to double count information from the two datasets, we restrict the range of ACT data following the procedure outlined in Ref. [CIT], i.e. we cut the TT likelihood at $\ell_{\rm min}=1800$ and use only higher multipoles. We only present results obtained for the combination of ACT and EG20, since running the P18 likelihood is computationally much more expensive. At low-$\ell$, we use both lowT and lowE[^16].

2108.10110

MISSION

We provide a refined and much more simplified Einstein-Gauss-Bonnet inflationary theoretical framework, which is compatible with the GW170817 observational constraints on the gravitational wave speed. As in previous works, the constraint that the gravitational wave speed is $c_T^2=1$ in natural units, results to a constraint differential equation that relates the coupling function of the scalar field to the Gauss-Bonnet invariant $\xi(\phi)$ and the scalar potential $V(\phi)$. Adopting the slow-roll conditions for the scalar field and the Hubble rate, and in contrast to previous works, by further assuming that $\kappa \frac{\xi '}{\xi''}\ll 1$, which is motivated by slow-roll arguments, we succeed in providing much more simpler expressions for the slow-roll indices and for the tensor and scalar spectral indices and for the tensor-to-scalar ratio. We exemplify our refined theoretical framework by using an illustrative example with a simple power-law scalar coupling function $\xi(\phi)\sim \phi^{\nu}$ and as we demonstrate the resulting inflationary phenomenology is compatible with the latest Planck data. Moreover, this particular model produces a blue-tilted tensor spectral index, so we discuss in brief the perspective of describing the NANOGrav result with this model as is indicated in the recent literature.

2108.10460

MISSION

However, the properties of the PQ axion change in higher-dimensional theories of low-scale quantum gravity [CIT]. The hierarchy between the gravitational and Planck scale could be explained if $n$ extra compact dimensions exist through which gravity, but not the Standard Model particles, can propagate. In that case, the Planck scale $M_P$ is just an effective coupling, related to the scale of $(n=4)$ dimensional gravity by: $M_P^2 = 4\pi R^n M_F^{2+n}$ where $R$ is the compactification radius of the extra dimensions and $M_{F}$ is the fundamental quantum-gravity scale. The axion, propagating through these additional dimensions, would obtain a tower of excitations of much higher mass, named Kaluza-Klein (KK) axions, evenly spaced out in mass by a factor of $1/R$. For two additional dimensions and $M_F\sim100,\mathrm{TeV}$, one obtains $1/R \sim 1,\mathrm{eV}$ [CIT]. These excitations would have much shorter lifetimes:

2109.03562

UNITS, UNITS

The relic abundance of a dark matter particle $\rm DM$, which was in thermal equilibrium at some earlier epoch can be calculated by solving the Boltzmann equation FORMULA where $n_{\rm DM}$ is the number density of the dark matter particle $\rm DM$ and $n^{\rm eq}_{\rm DM}$ is the number density when $\rm DM$ was in thermal equilibrium. $H$ is the Hubble expansion rate of the Universe and $\langle \sigma v \rangle$ is the thermally averaged annihilation cross section of the dark matter particle $\rm DM$. In terms of partial wave expansion $\langle \sigma v \rangle = a +b v^2$. Numerical solution of the Boltzmann equation above gives [CIT] FORMULA where $x_F = M_{\rm DM}/T_F$, $T_F$ is the freeze-out temperature, $M_{\rm DM}$ is the mass of dark matter, $g_*$ is the number of relativistic degrees of freedom at the time of freeze-out and and $M_{\text{Pl}} \approx 2.4\times 10^{18}$ GeV is the Planck mass. Dark matter particles with electroweak scale mass and couplings freeze out at temperatures approximately in the range $x_F \approx 20-30$. More generally, $x_F$ can be calculated from the relation FORMULA which can be derived from the equality condition of DM interaction rate $\Gamma = n_{\rm DM} \langle \sigma v \rangle$ with the rate of expansion of the Universe $H \approx g^{1/2}_*\frac{T^2}{M_{Pl}}$. The thermal averaged annihilation cross section $\langle \sigma v \rangle$ used in Boltzmann equation of REF(#eq:dmbe1){reference-type="eqref" reference="eq:dmbe1"} is given by [CIT] FORMULA where $K_i$'s are modified Bessel functions of order $i$, $m$ is the mass of Dark Matter particle and $T$ is the temperature.

2109.05417

UNITS

Recently [CIT] (hereafter Y21) identified $\sim 10^7$ galaxy groups from the DESI imaging surveys [CIT], over $\sim 20,000$ deg$^2$ and $z<1$. Compared with the majority of galaxies in the DESI imaging surveys, these galaxy groups have better photo-$z$ information and less imaging systematics, making them attractive in CMB lensing-LSS cross-correlation measurement. Furthermore, Y21 also provides an estimation of the halo mass. Such information is crucial in validating/interpreting the cross-correlation measurement. For these reasons, we measure the cross-correlation between the galaxy group positions (number density) of the Y21 catalog and Planck CMB lensing [CIT]. With $\sim$ 40% overlapping sky coverage and $2 \times 10^6$ galaxy groups of richness $N_{\rm g}\geq 5$ over $0.1<z<1.0$, we detect the cross-correlation signal with S/N $\simeq$ 40. The S/N increases to $50$ if we relax the richness cut to $N_{\rm g}\geq 2$. Thanks to a large number of clusters and groups, we have improved the S/N of cluster/group-CMB cross-correlation measurement by a factor $\ga 5$, over previous measurements [CIT]. An important improvement to previous works is that, we are now able to directly compare the measured group bias $b_{\rm g}$ with the theoretically predicted one using the estimated halo mass of each group. The agreement is excellent for the two higher redshift bins.

2109.07387

MISSION

Having described above the key physics inputs, in this section we will derive an exact wave function of the universe, in the presence of shear, by solving REF. For this purpose and also for future manipulations, it is convenient to rewrite REF in the following form: FORMULA where, we have introduced the parameters $\sigma$ and $\alpha_{n}$ through the following definitions: FORMULA where, we have defined the 'Planck length', 'Planck density' and 'Planck volume', respectively, as $\ell_{\rm Planck}=\sqrt{\hbar\kappa/3}$, $\rho_{\rm Planck}\equiv \hbar\ell_{\rm Planck}^{-4}$ and $V_{\rm Planck}=\ell_{\rm Planck}^3$. The reduced Wheeler-deWitt equation, as presented in REF, resembles the Schrödinger equation with a harmonic oscillator and an inverse harmonic oscillator potential, which with appropriate substitution can be exactly solved (for more details, see [7]. This is what we will do in the subsequent discussion. After deriving the wave function, we will apply the appropriate boundary conditions, presented in REF, in order to determine the probabilities of bounce and collapse in the presence of shear.

2109.08696

UNITS, UNITS, UNITS, CONSTANT, CONSTANT, CONSTANT, CONSTANT, CONSTANT

However, a complementary approach toward the realization of a quantum gravity theory can be represented by a bottom up strategy where the possible scenarios of a low-energy (sub-Planck scale) limit of quantum gravity are considered and put to the observational/experimental tests. In particular, it is expected that the transition from a full quantum and discrete spacetime to the standard classical continuum one, will not happen abruptly but will give rise to a mesoscopic regime where a continuum spacetime is endowed with different local symmetries due to remnant structure inherited from the super-Planckian regime. Deviation from standard Lorentz invariance is the most investigated scenario (but not the only one, see e.g. [CIT]). In this respect there are two main scenarios: one can consider that for high energies a Lorentz invariance violation (LIV) [CIT] can arise, or that the symmetry is deformed, leading to the theories known as deformed special relativity (DSR) [CIT].

2109.12336

UNITS

5. **constraint on $r$:** To show how good our methods are, we also use the calculated unbiased clean spectra to constraint the tensor to scalar ratio $r$. The full posterior for the individual band powers is non-Gaussian. However, for high enough multipoles (usually $\ell\ge30$) the central limit theorem justifies a Gaussian approximation [CIT]. The lowest multipole $\ell$ in our binning scheme is $30$ thus the Gaussian approximation is valid: FORMULA where the observed power spectrum is denoted as $\hat{C}_{\ell_b}^{BB}$. $C_{\ell_b}^{BB}$ denotes the theoretical power spectrum which was calculated by `CAMB` code. The likelihood only concerns the $BB$ spectra at $\ell\ge30$, where the primordial gravitational wave and lensing effect matters, so we fixed all the parameters to the best fit value from Planck-2018 [CIT], while only free $r$ and $A_L$. The covariance term is estimated from the signal+noise simulations. We sample this likelihood for these two parameters using the `CosmoMC` [CIT] [^3] package. The posteriors are summarized by `GetDist` [CIT] [^4] package.

2109.12619

MISSION

[^1]: The LBT is an international collaboration among institutions in the United States, Italy and Germany. LBT Corporation partners are: The University of Arizona on behalf of the Arizona university system; Istituto Nazionale di Astrofisica, Italy; LBT Beteiligungsgesellschaft, Germany, representing the Max-Planck Society, the Astrophysical Institute Potsdam, and Heidelberg University; The Ohio State University, and The Research Corporation, on behalf of The University of Notre Dame, University of Minnesota and University of Virginia.

2109.12971

MPS

Having established $\phi_+$ as the relevant function, the total energy of a tetron-(anti)tetron system is given by $E(L)+A(L)$, where the direct energy $|E|\sim 10^{19}$ GeV (corresponding to the Planck energy) is many orders of magnitude larger than the 'isomagnetic' exchange energy $|A|\sim 100$ GeV (determining the electroweak symmetry breaking). This hierarchy arises from the 12-dimensional integration, because the exchange energy is strongly dependent on the overlap of wave functions. One can calculate numerically $A(L)$ and $E(L)$ for the smoothed-out Lennard-Jones potential and some trial wave functions $\phi_1$ and $\phi_2$ of two tetrons 1 and 2 centered at distance $L$, and finds that ist is not unreasonable that each of the 12 integrations contributes about a factor of 0.05 to the ratio A/E.

2110.05958

UNITS

As more data are independently collected by current galaxy surveys, the slight tension in $S_8$ between CMB and cosmic shear surveys does not seem to disappear. More specifically, all results coming from the Dark Energy Survey (DES, [CIT] -DES-Y1 [CIT]) and the Hyper Supreme Camera (HSC, [CIT] -Hikage-HSC) indicate a lower value for the amplitude of matter density fluctuations, consistent with the Kilo Degree Survey (KiDS, [CIT] -Hidelbrandt-KV450 [CIT]), but also consistent with the Planck projections at a $\gtrsim 1.6 \sigma$ level. Combining a subset of these independent surveys, which all use different instruments and observing strategies, the tension with the early Universe probes is exacerbated. In a re-analysis of DES first year data combined with KiDS, [CIT] demonstrate that the tension can be around 3.2$\sigma$ between cosmic shear and CMB measurements from Planck. These consistent results from different experiments encourage us to believe that it is unlikely that this tension arises from an observational systematic error; however, there is still room for different explanations [CIT]. From a similar perspective, recent results from the Atacama Cosmology Telescope (ACT), a ground-based CMB experiment, observe a similar tension in $S_8$ with cosmic shear probes when combined with other CMB experiments [CIT]. This also suggests that it is unlikely that the tension we currently observe comes from a systematic contamination in the CMB experiments. If this discrepancy between measurements is indeed induced by systematic contamination, it would have to be shared across several independent datasets with widely different properties and analysis choices. Hopes are that experiments planned for the near future will shine a light on this interesting cosmic puzzle as there is still room to improve the precision on cosmic shear experiments.

2110.06947

MISSION, MISSION

To compare the predictions of the Weyl cosmological model to the $\Lambda$CDM model, we adopt for the density parameters the values $\Omega_{DM}= 0.2589\pm 0.0057$, $\Omega _{b}= 0.0486\pm 0.0010$, and $\Omega _{\Lambda}=0.6911\pm 0.0062$, respectively, which follow from the Planck data [CIT]. Hence, the total matter density $\Omega _m=\Omega _{DM}+ \Omega _b\approx 0.31$. With the help of the density parameters we obtain for the present-day value of the deceleration parameter the value $q(0)=-0.5381$. This indicates that at present the Universe is in an accelerating phase. In our comparison below of the Weyl model versus $\Lambda$CDM we also include the observational data for the redshift dependence of the Hubble function, by using the data quoted in Table IV of [CIT] (see references therein for the observational results and their error bars).

2110.07056

MISSION

SDSS-IV is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS Collaboration including the Brazilian Participation Group, the Carnegie Institution for Science, Carnegie Mellon University, Center for Astrophysics \| Harvard & Smithsonian, the Chilean Participation Group, the French Participation Group, Instituto de Astrofísica de Canarias, The Johns Hopkins University, Kavli Institute for the Physics and Mathematics of the Universe (IPMU) / University of Tokyo, the Korean Participation Group, Lawrence Berkeley National Laboratory, Leibniz Institut für Astrophysik Potsdam (AIP), Max-Planck-Institut für Astronomie (MPIA Heidelberg), Max-Planck-Institut für Astrophysik (MPA Garching), Max-Planck-Institut für Extraterrestrische Physik (MPE), National Astronomical Observatories of China, New Mexico State University, New York University, University of Notre Dame, Observatário Nacional / MCTI, The Ohio State University, Pennsylvania State University, Shanghai Astronomical Observatory, United Kingdom Participation Group, Universidad Nacional Autónoma de México, University of Arizona, University of Colorado Boulder, University of Oxford, University of Portsmouth, University of Utah, University of Virginia, University of Washington, University of Wisconsin, Vanderbilt University, and Yale University.

2110.10694

MPS, MPS, MPS

Quantization of linearized GWs is usually done within the framework of quantum field theory (QFT), where the GW field is simply treated as a rank-$2$ tensor possessing $2$ different polarization states [CIT]. With the help of the classical Lagrangian (REF), we define the canonical conjugate momentum of $h_{ij}$, as $\Xi_{ij} \equiv \partial \mathcal{L}_{\text{gw}}/\partial \dot{h}_{ij} =c^2/(32\pi G) \dot{h}_{ij}$. In quantum description, one promotes $h_{ij}$ and $\Xi_{ij}$ to operators, FORMULA FORMULA where $K\equiv(\gamma,\mathbf{K})$ and the constant $A$ has to be determined. The bosonic operators $(\hat{b}_{K},\hat{b}_{K}^{\dagger})$ are the ladder operators of mode $K$. Following the standard QFT approach, we impose the following equal time commutation relation between $h_{ij}$ and its conjugate momentum, FORMULA By plugging (REF, REF) into (REF) one gets $A=\sqrt{16 \pi c} \ell_{\text{Pl}}$ [CIT], where $\ell_{\text{Pl}}=\sqrt{\hbar G/c^3}$ is the Planck length, and the bosonic commutation relation $[\hat{b}_{K},\hat{b}_{K'}^{\dagger}] = \delta_{\gamma\gamma'}\delta^{(3)}(\mathbf{K}-\mathbf{K}')$ outcomes. The free Hamiltonian of GWs turns out to be FORMULA Substituting (REF, REF) into the Hamiltonian (REF) one gets FORMULA

2110.10962

UNITS

The study of cosmic inflation with the scalar singlet as the inflaton in minimal $B-L$ has been performed earlier in [CIT]. Further extension of the minimal $B-L$ model with a discrete symmetry $Z_2$ can provide a stable dark matter candidate which is the lightest RH neutrino. An attempt to simultaneous realisation of inflation and cold dark matter (both thermal and non-thermal) considering minimal $U(1)_{B-L}$ model has been performed in [CIT]. In this work, we envisage the scope of realizing warm dark matter in a $B-L$ inflationary framework which also offers correct magnitude of spectral index and tensor to scalar ratio in view of most recent Planck 2018+BICEP/Keck data [CIT] published in 2021. For the purpose we have added a new gauge singlet vector like fermion (serving as the DM candidate) to the minimal gauged $B-L$ model. Such extension is desirable for simultaneous explanation of correct WDM relic and active neutrino masses satisfying neutrino oscillation data as we explain in upcoming sections.

2110.13927

MISSION

The limit [Eq. (REF)] is $13$ times better than the previous one obtained with a dedicated experiment, MURMUR [CIT]. The main reasons for this improvement are the source configuration and a factor hundred lower counting rate per volume unit, thanks to a better shielding. Figure REF shows the corresponding exclusion contour in the ($\varepsilon$,$\Delta E$) parameter space, obtained using Eq. (REF), compared with the contours of the MURMUR experiment [CIT], ultra cold neutrons (UCN) experiments [CIT], and a cold neutron experiment at the Spallation Neutron Source SNS [CIT]. In braneworld approaches, $\Delta E$ naturally merges with the difference of gravitational potential energies felt by the neutron in each brane [CIT]. Using recent data [CIT], the expected value is around $\Delta E=2$ keV. It can also be shown that the maximum expected value of the coupling parameter is $\varepsilon =2.9$ meV if the brane energy scale equals the Planck energy [CIT]. With a new experimental upper limit $\varepsilon(\Delta E=2$ keV$) =7.9$ meV, the [Stereo]{.smallcaps} experiment gets close to the expected values.

2111.01519

UNITS

$^1$CRESST and X-ray Astrophysics Laboratory, NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA\ $^2$Max Planck Institute for Extraterrestrial Physics, Germany\ $^3$Cahill Center for Astronomy and Astrophysics, California Institute of Technology, USA\ $^4$Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, USA\ $^5$ESA-ESTEC, The Netherlands\ $^6$Center for Astrophysics $|$ Harvard & Smithsonian (CfA), USA\ $^7$IAPS-INAF, Italy\ $^8$Saitama University, Japan\ $^9$Japan Aerospace Exploration Agency, Institute of Space and Astronautical Science, Japan

2111.01613

MPS

NIKA2 is perfectly suited for this endavour as it combines high-angular resolution at 150 and 260 GHz with a large field-of-view, enabling esquisite resolved SZ mapping of clusters. This will be done in the framework of the LPSZ, a NIKA2 Guaranteed-Time Large Program dedicated to the observations of a representative sample of 45 SZ-selected clusters at $0.5 < z < 0.9$ from the Planck and ACT catalogs (300 hours, PI: F. Mayet, co-PI: L. Perotto).

2111.01729

MISSION

SDSS-IV is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS Collaboration including the Brazilian Participation Group, the Carnegie Institution for Science, Carnegie Mellon University, the Chilean Participation Group, the French Participation Group, Harvard-Smithsonian Center for Astrophysics, Instituto de Astrofísica de Canarias, The Johns Hopkins University, Kavli Institute for the Physics and Mathematics of the Universe (IPMU) / University of Tokyo, the Korean Participation Group, Lawrence Berkeley National Laboratory, Leibniz Institut für Astrophysik Potsdam (AIP), Max-Planck-Institut für Astronomie (MPIA Heidelberg), Max-Planck-Institut für Astrophysik (MPA Garching), Max-Planck-Institut für Extraterrestrische Physik (MPE), National Astronomical Observatories of China, New Mexico State University, New York University, University of Notre Dame, Observatário Nacional / MCTI, The Ohio State University, Pennsylvania State University, Shanghai Astronomical Observatory, United Kingdom Participation Group, Universidad Nacional Autónoma de México, University of Arizona, University of Colorado Boulder, University of Oxford, University of Portsmouth, University of Utah, University of Virginia, University of Washington, University of Wisconsin, Vanderbilt University, and Yale University.

2111.03156

MPS, MPS, MPS

Fig. REF shows the combined constraints from the combination of KiDS-450 + BOSS +eBOSS (orange contours), which are in near-perfect agreement with the equivalent combination using DES (grey contours). The suspiciousness statistic shows an agreement between Planck and this set of low-redshift measurements of $1.5 \pm 0.5 \sigma$, which is also consistent with our results from BOSS + eBOSS + DES.

2111.03156

MISSION

The spectral index distribution for each population is estimated in Planck at each frequency [CIT]. For frequencies below 217 GHz, the emission is mostly due to radio galaxies. Above such a frequency, most of the contribution comes from the late-type galaxies. At 217 GHz, the emission of both kind of sources is relevant to the total distribution. In our simulations, the spectral index is randomly chosen according to the gaussian distributions with mean and standard deviation given in [CIT].

2111.04075

MISSION

The data were correlated at the Max-Planck-Institut für Radioastronomie (MPIfR) using the DiFX software correlator [CIT], which had been modified to include a model for the path delay of an interferometer including an orbiting element by taking into account both special and general relativistic effects in a rigorous manner [CIT]. Post-correlation analysis was performed in two steps in order to deal with specific issues of space-VLBI data.

2111.04481

MPS

Mergers of compact object binary systems can also be used as standard sirens to estimate the Hubble constant [CIT]. This can be exploited to test a feature shared by many [QG]{acronym-label="QG" acronym-form="singular+short"}, namely a non-perturbative effect which underlines the way the dimension of spacetime changes with the probed scale. This dimensional flow influences the [GW]{acronym-label="GW" acronym-form="singular+short"} luminosity distance, the time dependence of the effective Planck mass, and the instrumental strain noise of interferometers. Investigating the consequences of [QG]{acronym-label="QG" acronym-form="singular+short"} dimensional flow for the luminosity distance scaling of [GW]{acronym-label="GW" acronym-form="singular+short"} s in the frequency ranges of LIGO and [LISA]{acronym-label="LISA" acronym-form="singular+short"}, it was shown that the quantum geometries of [GFT]{acronym-label="GFT" acronym-form="singular+short"}, spin foams and [LQG]{acronym-label="LQG" acronym-form="singular+short"} can give rise to observable signals in the [GW]{acronym-label="GW" acronym-form="singular+short"} spin-2 sector [CIT].

2111.05659

UNITS

While we include all the data points in the SED plots, we did not use the Planck $217$,GHz band in fitting since these bands are affected by Galactic CO(1--0) and CO(2--1) transitions. For future work we will attempt to include these frequencies by subtracting the Planck internal estimate of Galactic CO emission [CIT].

2111.05932

MISSION, MISSION

[^3]: Ref. [CIT] provides limits on DM mass through joint analyses by combining the Planck data with the local measurement of $H_0$ [CIT] (Planck$+H_0$), or with the measurements of the primordial abundances of light nuclei [CIT] (Planck$+{\rm BBN}$). Each joint analysis prefers larger values of $N_{\rm eff}$ compared to the analysis of the Planck data alone for non-annihilating DM. This is because of the apparent tension on the determination of $H_0$ from local measurements and Planck data, and the slight $\sim 0.9,\sigma$ tension on the inferred $\Omega_b h^2$ between BBN and CMB observations [CIT]. Since electrophilic DM lowers $N_{\rm eff}$, joint analyses provide stronger limits on the masses of electrophilic DM; for complex scalar DM, the limits are $m_{\rm dm}\gtrsim 9.2,{\rm MeV}$ for Planck$+H_0$ and $m_{\rm dm}\gtrsim 8.1,{\rm MeV}$ for Planck$+{\rm BBN}$. To be conservative, we take the limit from Planck data alone.

2111.06808

MISSION, MISSION, MISSION, MISSION, MISSION, MISSION, MISSION, MISSION

For some parameter fits, we also include measurements of the CMB TT, TE and EE power spectra from the 2018 data release of the Planck satellite [CIT]. We refer to this dataset as 'Planck' throughout rest of the work. The Planck CMB data allow us to demonstrate where clusters and CMB-cluster lensing add the most information.

2111.07491

MISSION, MISSION, MISSION

In this appendix, we will present an alternate solution to the Fokker-Planck equation FORMULA The basic idea is to use the Fourier transform to simplify the derivatives with respect to $\zeta$. Specifically, if we define FORMULA then the Fokker-Planck equation becomes FORMULA This can be integrated to obtain FORMULA To determine the probability distribution of $\zeta$, we take the inverse Fourier transform FORMULA For large $\texttt{t}$, we might suspect we can calculate this integral using the method of steepest descents. Specifically, we can deform the $k$ contour in the complex plane so that is goes through a point $k_\star$ such that FORMULA which occurs when FORMULA Noting $\gamma_3 \ll \Delta_\zeta$, we should take the $-$ solution, since it lies closer to the real axis. We will assume $8\pi^4 \gamma_3 \zeta/\texttt{t}\ll 1$ so that FORMULA The resulting probability distribution can be determined approximately by using $k = k_\star + \bar k$ FORMULA where $C$ and $\tilde C$ are constants. Here we used the fact the integrand is analytic in the region enclosed by contours $k \in (-\infty, \infty)$ and $\bar k\in (-\infty, \infty)$ to obtain our final result.

2111.09332

FOKKER, FOKKER

Most of the pixels seem to be consistent with a $\beta$ of $\simeq 1.5$, as suggested by [CIT]. The latter use low-resolution Planck images to constrain $\beta$, which amounts to $\beta\simeq 1.6$ in the Orion Nebula complex. The median of all pixels in our SED fit is $\beta$ of $\simeq 1.2$, but when including only pixels with $\tau_{160}>5\times 10^{-4}$, which comprise most of the visible structure, the median shifts to $\beta$ of $\simeq 1.4$. The peak values, around which the $\beta$ values are clustered, is $\beta\simeq 1.6$. Standard models, however, suggest $\beta\simeq 2$ [CIT]. The study of [CIT] suggests varying $\beta$ according to the environment (radiation field). We note that $\beta$ can be affected by the presence of an additional warm dust population in the hot gas and we determine low $\beta$ in the EON cavity. $\beta$ may vary with the grain composition, grain-size distribution, and with the presence of ices on the grains [e.g., [CIT]]. Extragalactic studies show systematic variations of $\beta$ with galactocentric radius, which may be linked to metallicity gradients [e.g., [CIT]].

2111.12363

MISSION

Optical and infrared polarization mapping and recent Planck observations of the filamentary cloud L1495 in Taurus show that the large-scale magnetic field is approximately perpendicular to the long axis of the cloud. We use the HAWC+ polarimeter on SOFIA to probe the complex magnetic field in the B211 part of the cloud. Our results reveal a dispersion of polarization angles of $36^\circ$, about five times that measured on a larger scale by Planck. Applying the Davis-Chandrasekhar-Fermi (DCF) method with velocity information obtained from IRAM 30m C$^{18}$O(1-0) observations, we find two distinct sub-regions with magnetic field strengths differing by more than a factor 3. The quieter sub-region is magnetically critical and sub-Alfv\'enic; the field is comparable to the average field measured in molecular clumps based on Zeeman observations. The more chaotic, super-Alfv\'enic sub-region shows at least three velocity components, indicating interaction among multiple substructures. Its field is much less than the average Zeeman field in molecular clumps, suggesting that the DCF value of the field there may be an underestimate. Numerical simulation of filamentary cloud formation shows that filamentary substructures can strongly perturb the magnetic field. DCF and true field values in the simulation are compared. Pre-stellar cores are observed in B211 and are seen in our simulation. The appendices give a derivation of the standard DCF method that allows for a dispersion in polarization angles that is not small, present an alternate derivation of the structure function version of the DCF method, and treat fragmentation of filaments.

2111.12864

MISSION, MISSION

Following the standard practice for radiation-hydrodynamics and newly-developed methods which evolve the Fokker-Planck equation for a population of CRs [CIT], we multiply this equation by $1/c$ but then ad-hoc replace the value $1/c$ *only* in front of the time derivative $\partial_{t} f$ with a different value $\tilde{c}$, to introduce the RSOL. FORMULA This is equivalent to taking $\partial_{t} f^{\rm rsol} = (\tilde{c}/c),\partial_{t} f^{\rm true}$ -- i.e. the time variation of $f$ is systematically slowed by a factor of $\tilde{c}/c$, equivalent to a rescaling of time "as seen by" the CRs. This is what allows us, fundamentally, to take larger timesteps by a factor $c/\tilde{c}$, as the time variation is slower. But this also ensures that one still recovers *exactly* the correct steady-state solutions ($\partial_{t} f \rightarrow 0$) for the distribution function $f$, independent of the choice of $\tilde{c}$.

2111.14704

FOKKER

[^5]: In practice, such a first-passage-time distribution can still be computed by solving the adjoint Fokker--Planck equation REF(#eq: adjoint FP){reference-type="eqref" reference="eq: adjoint FP"} with an absorbing condition at $\bm{\Phi}_*$, by adding a "trapping" boundary along the end-of-inflation surface (for instance setting the potential to $0$ on that surface, such that the fields cannot escape the trap). The trajectories that do not cross $\bm{\Phi}_*$ end up at the bottom of the trap, hence they do not contribute to finite values of $\mathcal{N}$ in the first-passage time distribution, which simply needs to be renormalised to account for those missing trajectories.

2111.15280

FOKKER

where $x=m_\chi/T$ and $Y_i= n_i/s$, with number density $n_i$ and entropy density $s$, with FORMULA where $M_\text{pl}\simeq 2.4 \times 10^{18},$GeV is the reduced Planck mass. $Y_{\tilde q}$ represents the summed contribution of the mediator and its anti-particle, FORMULA leading to the various factors $1/2$. Here, $g_{\tilde q}=g_{\tilde q^\dag}=N_c=3$, and $f_{\tilde q}$ is the distribution function that is assumed to be identical for particles and antiparticles as well as all colors. The processes in the first line of each equation denote the usual (co-)annihilation processes into SM particles.

2112.01499

UNITS

Observations of cosmic microwave background (CMB) anisotropies have played a major role in shaping up our current view of the Universe, its composition and evolution. This has been epitomized by the results obtained by the Planck satellite [CIT], which, with complementary information provided by other probes, have established the current standard cosmological model determining its parameters with a few percent precision. The scientific potential of the CMB has not been exhausted yet and only experiments forthcoming on the timescale of this decade are expected to exploit the full scientific information contained in the polarization properties of the CMB anisotropies. This is expected to open a new window on the evolution and physics of the very early Universe providing unique insights about physical laws at extremely high energies exceeding by many orders of magnitude energies accessible by any current and projected human-made experiments. The potential impact of these new experiments is therefore difficult to overestimate.

2112.03370

MISSION

The gravitational interaction of a fermionic matter field $\psi(x)$ in the traditional 3+1-dimensional space-time ${\cal M}^4$ is described by the Einstein-Dirac action FORMULA where $x= (x^0, x^1, x^2, x^3), a= \dot 0,\dot 1,\dot 2,\dot 3; \mu = 0,1,2,3$. The dotted integers are used for the flat index $a$ to avoid confusion. $e^a_\mu(x)$ is the traditional vierbein representing gravity, while $r_4$ is its Ricci scalar curvature. $M_{Planck}(4) = 1/ 4 \sqrt{\pi G_N}$ is the Planck mass, where $G_N$ is the Newton's gravitational constant. The spin connection $\omega_\mu(x)$ is necessary to make the derivative covariant.

2112.05015

UNITS, UNITS

We firstly estimate the value of $H_0$ using the Planck 2018 observations of the cosmic microwave background temperature anisotropies and polarisation. While neither the results obtained by the Gaussian Process Monte Carlo technique or the local measurement of $H_0$ provided by the S$H_0$ES collaboration rely on the precise form of $E^2(z)$, inferring the value of the present day expansion rate from observations of the early universe (*i.e.* the CMB) necessarily requires a cosmological model.

2112.05701

MISSION

The sensitivity of CMB lensing to $\mathrm{\Lambda CDM}$ cosmological parameters is discussed in [CIT]. There is a three parameter degeneracy $\sigma_8$ - $\Omega_{\rm m}$ - $H_0$ 'tube', which projects onto a tightly constrained $\sim \sigma_8 \Omega_{\rm m}^{0.25}$. For our lensing-only constraints, we use the same priors as the Planck analysis [CIT], most notably a prior on the baryon density from abundance measurements that constrains the sound horizon (a prior much weaker than the constraints expected from CMB-S4). The marginalized posterior on the CMB lensing parameter are shown in the lower panel of Fig. REF, where we also show for comparison the constraints from the Planck lensing-only analysis [CIT]. For both input cosmologies we recover an unbiased estimate of the $\sigma_8 \Omega_{\rm m}^{0.27}$ parameter combination, with constraints about seven times better than current best data (the 0.27 exponent was found with a principal component analysis of our chains).

2112.05764

MISSION, MISSION

We estimate the total hydrogen column density, $N_\mathrm{H}=N({\rm H,{\small I}}{})+2N(\text{H\textsubscript{2}}{})$, from the interstellar reddening, $E(B-V)$, FORMULA [CIT]. Here, $3.1E(B-V)$ is used as an estimate of the visual extinction, $A_V$. For each sightline, we extract $E(B-V)$, derived from the dust radiance measured by the Planck satellite [CIT], from the nearest pixel using the dustmaps Python package [CIT]. We also extract the dust temperature, $T_d$, from the maps derived by [CIT] based on a modified blackbody spectral model of Planck temperature maps at 353, 545, 857, and 3000 GHz. Since the dust temperature is set in part by the strength of the interstellar radiation field (ISRF), it can be used to estimate the strength of the radiation field, $\propto T_d^{\beta+4}$, where $\beta$ (also measured by Planck) is the power law index that describes the dust emissivity cross-section as a function of frequency [e.g., Equation 7.15 of [CIT]]. However, the dust temperature also depends on the grain size distribution, grain composition, and structure, which results in a more complex relationship between $T_d$ and the strength of the ISRF. Moreover, the resolution of the Planck dust maps is 5, so the values of $E(B-V)$, $T_d$, $\beta$, and the ISRF strength should only be considered as very rough estimates to the local properties of the gas sampled by our H,I and molecular pencil-beam absorption spectra. We also note that the estimates of $T_d$, $\beta$, and the ISRF strength derived from Planck observations are not included in our modeling; they are only discussed in Section [6] for context.

2112.05767

MISSION, MISSION, MISSION, MISSION, MISSION

The Pan-STARRS1 Surveys (PS1) and the PS1 public science archive have been made possible through contributions by the Institute for Astronomy, the University of Hawaii, the Pan-STARRS Project Office, the Max-Planck Society and its participating institutes, the Max Planck Institute for Astronomy, Heidelberg and the Max Planck Institute for Extraterrestrial Physics, Garching, The Johns Hopkins University, Durham University, the University of Edinburgh, the Queen's University Belfast, the Harvard-Smithsonian Center for Astrophysics, the Las Cumbres Observatory Global Telescope Network Incorporated, the National Central University of Taiwan, the Space Telescope Science Institute, the National Aeronautics and Space Administration under Grant No. NNX08AR22G issued through the Planetary Science Division of the NASA Science Mission Directorate, the National Science Foundation Grant No. AST-1238877, the University of Maryland, Eotvos Lorand University (ELTE), the Los Alamos National Laboratory, and the Gordon and Betty Moore Foundation.

2112.09930

MPS, MPS, MPS

For the Planck+SH0ES best-fit model of [CIT], the shift in $H_0$ falls just short of being detected at $3\sigma$; however, if we instead use that of the latest ACT analyses [CIT], the shift increases to $\approx 9\sigma$, due to the much larger EDE fraction. The results found herein demonstrate that our method can be used as a powerful null test for models of post-$\Lambda$CDM physics. Since many approaches claiming to resolve the so-called Hubble tension modify the physical size of the sound horizon at the end to the baryon drag epoch, it is generically expected that such models would affect the sound horizon and the equality scale differently, thus leading to an inconsistency of the two $H_0$ measurements.

2112.10749

MISSION

Since it has been shown that BHs emit quasi-thermally all particles in the "spectrum of Nature" [CIT], people have tried to extract a PBH signal from the observational data, without success so far. This absence of signal has been interpreted as a constraint on the PBH abundance over a wide range of masses. For an initial mass from the Planck scale $M_{\rm Pl} \approx 10^{-5},$g to some $M_{\rm min} = 10^{14},$g, PBHs would have already evaporated away by now, forbidding them to be a sizeable component of the DM today, but their Hawking radiation could have left imprints in the big bang nucleosynthesis element abundances or in the cosmic microwave background [CIT]. Above an initial mass of some $M_{\rm min}$, PBHs would still be around, filling the universe with all kind of radiation, from photons to hadronized jets.

2201.01265

UNITS

FORMULA The peculiarity of Eq. REF(#res_act){reference-type="eqref" reference="res_act"} now traces back at the level of the spin-foam dynamics to the definition of a $SU(2)$ group element encoding space-time curvature of the form $H^{\Lambda}\!=\!\exp (G \sqrt{\Lambda}, \tau_3 n^3)$. Finally, in Planck units, i.e. with $G=1$, the curvature group element introduced in Eq. REF(#eq:trace_loop){reference-type="eqref" reference="eq:trace_loop"} is recovered, i.e. FORMULA For a generic "quantum-group effective" irrep $j$, using the effectively induced Jones-Wenzl projector, the evaluation of the trace of $H_{\Lambda}$ provides the Chebyschev $\Delta_{2j}^{\Lambda}$ polynomial of degree-$2j$, evaluated in $\sqrt{\Lambda}$.\ We finally comment that the curvature group element $H_\Lambda$ converges to the unity of the group $U=e$ in the vanishing cosmological constant limit $\Lambda \rightarrow 0$. Hence the standard flat curvature constraint is recovered [CIT], which induces the convergence of the recoupling theory of $SU_q(2)$ to the standard recoupling theory of $SU(2)$.\

2201.01726

UNITS

We tested this pipeline on mocks built from the OuterRim N-body simulation and efficiently recovered the five cosmological parameters with good accuracy and precision. Then, we analysed three samples of the SDSS spectroscopic surveys both individually and jointly, namely the BOSS low-z galaxy sample and the eBOSS LRG and QSO samples. The analysis of the QSO sample leads to a $\sigma_8$ value significantly different from that predicted from the Planck constraints [CIT]. This bias is also visible in the standard analysis [CIT], with a $2\sigma$ deviation from the Planck analysis when fixing the linear growth rate of structure to the GR expectation. Nevertheless, this discrepancy is reinforced in the present study and reaches a $3.1\sigma$ significance. All other parameters are in good agreement with the constraints from the CMB analysis.

2201.04679

MISSION, MISSION

The stochastic order redshift technique (SORT) is a simple, efficient, and robust method to improve cosmological redshift measurements. The method relies upon having a small ($\sim$10 per cent) reference sample of high-quality redshifts. Within pencil-beam-like sub-volumes surrounding each galaxy, we use the precise dN/d$z$ distribution of the reference sample to recover new redshifts and assign them one-to-one to galaxies such that the original rank order of redshifts is preserved. Preserving the rank order is motivated by the fact that random variables drawn from Gaussian probability density functions with different means but equal standard deviations satisfy stochastic ordering. The process is repeated for sub-volumes surrounding each galaxy in the survey. This results in every galaxy with an uncertain redshift being assigned multiple "recovered" redshifts from which a new redshift estimate can be determined. An earlier paper applied SORT to a mock Sloan Digital Sky Survey at $z \lesssim$ 0.2 and accurately recovered the two-point correlation function on scales $\gtrsim$4 $h^{-1}$Mpc. In this paper, we test the performance of SORT in surveys spanning the redshift range 0.75$<z<$2.25. We used two mock surveys extracted from the Small MultiDark-Planck and Bolshoi-Planck N-body simulations with dark matter haloes that were populated by the Santa Cruz semi-analytic model. We find that SORT is able to improve redshift estimates and recover distinctive large-scale features of the cosmic web. Further, it provides unbiased estimates of the redshift-space two-point correlation function $\xi(s)$ on scales $\gtrsim$2.5 $h^{-1}$Mpc, as well as local densities in regions of average or higher density. This may allow improved understanding of how galaxy properties relate to their local environments.

2201.05258

MISSION, MISSION

Funding for SDSS-III has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, and the U.S. Department of Energy Office of Science. The SDSS-III web site is http://www.sdss3.org/. SDSS-III is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS-III Collaboration including the University of Arizona, the Brazilian Participation Group, Brookhaven National Laboratory, Carnegie Mellon University, University of Florida, the French Participation Group, the German Participation Group, Harvard University, the Instituto de Astrofisica de Canarias, the Michigan State/Notre Dame/JINA Participation Group, Johns Hopkins University, Lawrence Berkeley National Laboratory, Max Planck Institute for Astrophysics, Max Planck Institute for Extraterrestrial Physics, New Mexico State University, New York University, Ohio State University, Pennsylvania State University, University of Portsmouth, Princeton University, the Spanish Participation Group, University of Tokyo, University of Utah, Vanderbilt University, University of Virginia, University of Washington, and Yale University.

2201.06612

MPS, MPS

The relative orientation between the two magnetic field directions probed with the Planck polarization ($\phi_B$) and the gradients ($\psi_B$) is measured with the Alignment Measure (AM; [CIT]), defined as FORMULA where we have $\theta_r = \vert\phi_B-\psi_B\vert$ and $\langle...\rangle$ denote averaging over a region of interests. AM is a relative scale ranging from -1 to 1, with AM = 1 indicating that $\phi_B$ and $\psi_B$ being globally parallel, and AM = -1 denoting that the two are globally orthogonal. Note that the VGT has a higher resolution (i.e., smaller scale) than the Planck measurement. The difference in resolutions may introduce uncertainty to the AM.

2201.07970

MISSION, MISSION

The blind PT challenge was designed by [CIT] with the aim to provide a controlled means of testing and benchmarking theoretical models for summary statistics of galaxy redshift surveys with a particular focus on each model's or approach's ability to recover and constrain cosmological parameter within $\Lambda$CDM. For that purpose, they carried out a suit of simulations consisting in 10 realizations (which we will later refer to as \# 1,.., 10, each of these representing a different realization of the initial conditions at a given cosmology) in cubes of comoving side length $3840 \left[h^{-1}\mathrm{Mpc}\right]$ with $3072^3$ particles, where the 3 input $\Lambda$CDM parameters, $\Omega_\mathrm{m}, A_s$ and $H_0$, were randomly selected from a Gaussian probability distribution centered at the Planck fiducial cosmology with a width of $4\sigma$ of the Planck experiment. These randomly drawn values (which are the same for the 10 simulations) were kept secret (blind) and not known to us or any of the participants. Other cosmological parameters such as the primordial tilt and the baryon-to-matter ratio were fixed to $\Omega_\mathrm{b}/\Omega_\mathrm{m}= 0.1571$ and $n_s = 0.9649$.

2201.08400

MISSION, MISSION

We reverse the logic behind the apparent existence of $H_0$-tension, to design diagnostics for cosmological models. The basic idea is that the non-constancy of $H_0$ inferred from observations at different redshifts is a null hypothesis test for models within the FLRW paradigm -- if $H_0$ runs, the model is wrong. Depending on the kind of observational data, the most suitable form of the diagnostic can vary. As examples, we present two $H_0$ diagnostics that are adapted to two different BAO observables. We use these and the corresponding BAO data to Gaussian reconstruct the running of $H_0$ in flat $\Lambda$CDM with Planck values for the model parameters. For flat $\Lambda$CDM when the radiation contribution can be neglected, with comoving distance data, the diagnostic is a simple hypergeometric function. Possible late time deviations from the FLRW paradigm can also be accommodated, by simply keeping track of the (potentially anisotropic) sky variation of the diagnostic.

2201.13384

MISSION

Relative gains across the detector array and between observations are measured using regular observations of the Galactic HII region RCW38 and regular observations of an internal thermal calibration source. As in, the absolute calibration of the map was derived by comparing the full-season coadded maps with the Planck map of the same field. The SPT-ECS fields were taken at significantly higher levels of atmospheric loading compared to other SPTpol survey data, and the resulting larger change in detector loading with elevation necessitated a further calibration step beyond a constant normalization factor for 3.2 mm data. Although noise in SPTpol data does not in general depend strongly on airmass, the 3.2 mm data required this additional calibration step as the calibration was empirically found to vary significantly with elevation within a field (which is equivalent to decl. for observations from the South Pole). This trend is fit well as a linear function of decl., and used the Planck data to fit for and correct this variation across the fields.

2202.01406

MISSION, MISSION

We explore in detail the possibility of dynamical DE with a more general model-independent approach where we go beyond the CPL (Chevalier-Polarski and Linder) parameterization [CIT] where the dark energy equation of state $w$ evolves linearly with expansion factor $a$. To be specific, in this paper, we study a generic non-linearly evolving equation of state. Some of the recent works on dynamical dark energy scenario such as [CIT] suggest that CPL parameterization is not sensitive at low redshifts and thus provide motivation for going beyond CPL like parameterization. It was recently pointed out that if late-time cosmology is modified through time-varying w, one indeed should use the direct prior on the absolute magnitude of supernovae, $M_B$ instead of $H_0$ prior [CIT]. To our knowledge, this work is the first work where we present a detailed analysis of a four parameter dynamical DE model. To do so, we use a generic four parameter model of dynamical dark energy equation of state $w$ originally proposed in [CIT] and test it against the recent Planck-2018, Pantheon and BAO datasets. In comparison to CPL parameterization, this parameterization has two extra parameters to incorporate the possible non-linear evolution of the equation of state with time. The main interest of this parameterization is that it captures possible transition in the equation of state of the dynamical dark energy during the course of its evolution, which many quintessence/K-essence and phantom dark energy models exhibit [CIT].

2202.01749

MISSION

4. *Hemispherical asymmetry.* The standard cosmological model predicts that the same power spectrum should be measured in different patches of the sky, except for variations connected with sample variance. However, *WMAP*and Planck data show evidence for a hemispherical asymmetry (or dipolar modulation) of power in a particular direction. For the Planckdata in particular, several methods to test for such asymmetry have been applied and compared [CIT]. These are sensitive to either amplitude, directionality, or both, although they do differ in terms of their weighting of power on different scales. Nevertheless, the results are all consistent with a modulation of power of around 7,% between two hemispheres defined by the preferred direction $(l,b) = (209^{\circ},-15^{\circ})$, extending over scales to $\ell_\mathrm{max}\simeq 60$ with a significance approaching $3,\sigma$. Interestingly, one such test, based on the anomalous clustering of directions within bands of multipoles, suggests that this asymmetry holds even to relatively small scales.

2202.02773

MISSION, MISSION

The emission properties of dust at long wavelengths have been shown by Planckto vary throughout the ISM [CIT]. Likewise, the alignment efficiency depends on both the local physical conditions and the dust composition [CIT]. Variations in dust emission properties and alignment efficiency are likely to be correlated with the density structure of the ISM, which in turn is known to be correlated with the magnetic field structure. These couplings break the simple assumption where the spectral frequency dependence of the Galactic polarization and its angular structure on the sky are separable. If a line of sight intercepts multiple dust clouds with different spectral energy distributions and magnetic field orientations, the frequency scaling of each of the Stokes $Q$ and $U$ parameters of the thermal dust emission may be different. Evidence for this effect has been reported using Planckdata [CIT]. In this context, the interpretation of *LiteBIRD*data in terms of dust properties in polarization will need to be coupled with the modeling of the 3D structure of the Galactic magnetic field.

2202.02773

MISSION, MISSION

**ACT DR4**: We use the multifrequency TT, EE, and TE power spectra from ACT Data Release 4 (DR4) [CIT], implemented within the `actpollite_dr4` likelihood [^5]. These data products are derived from a four--year survey, with the power spectrum measurements reconstructed from the deepest 5400 $\text{deg}^2$ of the sky. This data provide high resolution measurements of the polarization anisotropy, complementing the data from Planck. In the ACT likelihood, the covariance of the foreground--marginalized CMB power spectra already includes the effects of noise, foreground uncertainty, beam and calibration uncertainties, with one nuisance parameter $y_{p}$ included to marginalize over an overall polarization efficiency; we allow this variable to vary in a range centred at 1. ACT alone cannot constrain the optical depth to reionization $\tau$, as it is mainly determined by low--$\ell$ polarization power spectra; thus, when analyzing ACT data alone, we assume a Gaussian prior on $\tau=0.065\pm 0.015$, following Ref. [CIT].

2202.03515

MISSION

The dust mass of the well-known supernova remnant (SNR) IC 443 is estimated from both the infrared emission and the visual extinction. With photometry to the images taken by \emph{Spitzer}, \emph{WISE}, \emph{IRAS}, \emph{AKARI} and \emph{Planck}, the spectral energy distribution (SED) of the dust is obtained after subtracting the synchrotron radiation and considering the spectral line emission. The dust mass is derived from fitting the SED by a two-component model, which results in a warm component of the temperature of $\sim$ 53 K and the mass of 0.1 $M_\odot$, and a cold component of the temperature of $\sim 17$ K and the mass of 46 $M_\odot$. On the other hand, the dust mass is derived to be $\sim$ 66 $M_\odot$ from the visual extinction of IC 443 which is identified from the 3D Bayestar extinction map and its coincidence with the infrared emission morphology. Roughly the dust mass derived from the infrared emission and the extinction agree mutually. However, the dust mass derived from the infrared emission can be adjusted to be more consistent with that from the extinction by using different dust opacity property or considering optically thick radiation. In addition, the distribution of dust temperature and mass is analyzed by fitting the SED pixel by pixel.

2202.05174

MISSION

shows our main results. As described above, we compute $\Delta \chi^2_\mathrm{eff}$ for different datasets and for the two Planck likelihoods, the reference `Plik` and the alternative `CamSpec`; for $\Lambda$CDM and with long-range neutrino interactions. In the former case, we follow the Planck analysis and assume $\sum m_\nu = 0.06$ eV [CIT]. In the latter, both the total neutrino mass $\sum m_\nu$ and the interaction strength $g m_\nu/M_\phi$ are free parameters to be determined by data. We also show the frequentist $p-$values for excluding $A_\mathrm{lens} = 1$. (Below, we further quantify the tension with the Akaike Information Criterion.)

2202.04656

MISSION, MISSION

A basic feature of this model which makes the quiescent multiverse distinct from similar models (like the quantum cosmological model of Vilenkin's [CIT], or Linde's chaotic self-regenerating inflationary universe [CIT]), is the preference of initial scalar field conditions of the form $\phi_0<O(1)$, so that no mini-universe bubbles can collapse to spacetime singularities of infinite density. This is shown in [CIT], where the time it takes for the scalar field (in the conformal frame of the cubic theory) to become infinite decays is FORMULA where $\lambda$ is the exponential scalar field potential coupling to $\phi$, so that for small initial values of the scalar field this time is long enough for inflation to take place. (We note that in other multiverse models, this time is vanishingly small). In fact, a more systematic analysis of the quiescent multiverse was given in Ref. [CIT] based on the behaviour of solutions of a cosmological Fokker-Planck equation, where it was shown that a quiescent multiverse model is a solution of an Ornstein-Uhlenbeck type of stochastic process for the scalar field potential of the cubic lagrangian.

2202.06536

FOKKER

Measurements of cosmic microwave background (CMB) anisotropies, such as those from Planck DR3 [CIT], have contributed significantly to the characterization of the initial conditions of the Universe. The tight CMB constraints to spatial curvature, isocurvature fluctuations, and primordial non-Gaussianity, all agree with predictions of the standard single field slow-roll models [CIT].

2202.08819

MISSION

The universal similarity action allows one to eliminate the overall scale of $\Phi$ and another scale from the problem. For example, one can fix the overall scales of $\mathcal{G}$ and $\Phi$, in which case one is left with the single scale set by $M_0$. Equivalently, one can eliminate the rescaled Planck mass by setting $M_0=1$ and the overall scale of $\Phi$, in which case one is left with the single scale set by $\mathcal{G}$. Notice that one cannot fix the scales of $M_0$ and $\mathcal{G}$ independently. Since $\Phi$ plays a distinguished role in this regard, it is natural to consider the stabilizer $T_{\mathrm{ren}}\simeq \mathbb{R}_{>0}$ of $\Phi$ in $T$ with respect to the universal similarity action: FORMULA This is the subgroup of $T$ which can be used to rescale $M_0$ and $\mathcal{G}$ once the scale of $\Phi$ has been fixed; it is the *renormalization group* considered in Section [3].

2202.13466

UNITS