The traditional distance ladder measures the standardized peak absolute magnitude M^B of Type Ia supernovae (SNIa). According to the SH0ES collaboration, the distance ladder value of M^B is highly discrepant with the value inferred from the cosmic microwave background (CMB) assuming the LCDM cosmology. This CMB-distance ladder tension is insensitive to the actual late time expansion history of the Universe. To derive a value of the Hubble constant H_0, from M^B requires a cosmological model. However, the magnitude-redshift relation of SNIa provides tight constrains the expansion history. As a consequence, uncertainties in the conversion of M^B into H_0 have no significant impact on the CMB-distance ladder tension. The tentative claim by the Dark Energy Spectroscopic Instrument collaboration for late time evolution of the dark energy equation of state does not alter this conclusion.

The power spectrum of unresolved thermal Sunyaev-Zeldovich (tSZ) clusters is extremely sensitive to the amplitude of the matter fluctuations. This paper present an analysis of the tSZ power spectrum using temperature power spectra of the cosmic microwave background (CMB) rather than maps of the Compton y-parameter. Our analysis is robust and insensitive to the cosmic infrared background. Using data from Planck, and higher resolution CMB data from the Atacama Cosmology Telescope and the South Pole Telescope, we find strong evidence that the tSZ spectrum has a shallower slope and a much lower amplitude at multipoles l > 2000$compared to the predictions of the FLAMINGO hydrodynamic simulations of the LCDM cosmology. Recent results on CMB lensing, cross-correlations of CMB lensing with galaxy surveys and full shape analysis of galaxies and quasars from the Dark Energy Spectroscopic Instrument suggests that this discrepancy cannot be resolved by lowering the amplitude of the matter fluctuations. An alternative possibility is that the impact of baryonic feedback in the FLAMINGO simulations is underestimated.

We investigate the degeneracy between the effects of ultra-light axion dark matter and baryonic feedback in suppressing the matter power spectrum. We forecast that galaxy shear data from the Rubin Observatory's Legacy Survey of Space and Time (LSST) could limit an axion of mass m = 10(-25) eV to be less than or similar to 5 per cent of the dark matter, stronger than any current bound, if the interplay between axions and feedback is accurately modelled. Using a halo model emulator to construct power spectra for mixed cold and axion dark matter cosmologies, including baryonic effects, we find that galaxy shear is sensitive to axions from 10(-27) to 10(-21) eV , with the capacity to set competitive bounds across much of this range. For axions with m similar to 10(-25) eV , the scales at which axions and feedback impact structure formation are similar, introducing a parameter degeneracy. We find that, with an external feedback constraint, we can break the degeneracy and constrain the axion transfer function, such that LSST could detect a 10(-25) eV axion comprising 10 percent of the dark matter at similar to 3 sigma significance. Direct reconstruction of the non-linear matter power spectrum provides an alternative way of analysing weak lensing surveys, with the advantage of identifying the scale-dependent features in the data that the dark matter model imposes. We advocate for dedicated cosmological hydrodynamical simulations with an axion dark matter component so that upcoming galaxy and cosmic microwave background lensing surveys can disentangle the dark matter-baryon transfer function.

This paper presents an alternative way of analysing baryon acoustic oscillation (BAO) distance measurements via rotations to define new quantities ${\cal D}<^>{\rm perp}$ and ${\cal D}<^>{\rm par}$. These quantities allow simple tests of consistency with the Planck $\Lambda$cold dark matter (Lambda CDM) cosmology.1 The parameter ${\cal D}<^>{\rm perp}$ is determined with negligible uncertainty from Planck under the assumption of $\Lambda$CDM. Comparing with measurements from the Dark Energy Spectroscopic Instrument (DESI), we find that the measurements of ${\cal D}<^>{\rm perp}$ from Data Release 2 (DR2) move into significantly better agreement with the Planck $\Lambda$CDM cosmology compared to DESI Data Release 1 (DR1). The quantity in the orthogonal direction ${\cal D}<^>{\rm par}$ provides a measure of the physical matter density in the $\Lambda$CDM cosmology. The DR2 measurements of ${\cal D}<^>{\rm par}$ remain consistent with Planck $\Lambda$CDM despite the substantial improvement in their accuracy compared to the earlier DR1 results. Comparing Planck and DESI BAO measurements, we find no significant evidence in support of evolving dark energy. We also investigate a rotation in the theory space of the $w_0$ and $w_a$ parametrization of the dark energy equation-of-state $w(z)$. We show that the combination of DESI BAO measurements and the CMB constrain $w(z=0.5) = -0.996 \pm 0.046$, very close to the value expected for a cosmological constant. We present a critique of the statistical methodology employed by the DESI collaboration and argue that it gives a misleading impression of the evidence in favour of evolving dark energy. An appendix shows that the cosmological parameters determined from the Dark Energy Survey 5 Year supernova sample are in tension with those from DESI DR2 and parameters determined by Planck.

Recent results from the Dark Energy Spectroscopic Instrument (DESI) collaboration have been interpreted as evidence for evolving dark energy. However, this interpretation is strongly dependent on which Type Ia supernova (SN) sample is combined with DESI measurements of baryon acoustic oscillations and observations of the cosmic microwave background radiation. The strength of the evidence for evolving dark energy ranges from similar to 3.9 sigma for the Dark Energy 5 year (DES5Y) SN sample to similar to 2.5 sigma for the Pantheon+ sample. The cosmology inferred from Pantheon+ sample alone is consistent with the Planck lambda cold dark matter (Lambda CDM) model and shows no preference for evolving dark energy. In contrast, the the DES5Y SN sample favours evolving dark energy and is discrepant with the Planck Lambda CDM model at about the 3 sigma level. Given these difference, it is important to question whether they are caused by systematics in the SN compilations. A comparison of SN common to both the DES5Y and Pantheon+ compilations shows evidence for an offset of similar to 0.04 mag between low and high redshifts. Systematics of this order can bring the DES5Y sample into good agreement with the Planck Lambda CDM cosmology and Pantheon+. I comment on a recent paper by the DES collaboration that rejects this possibility.

Observations of the cosmic microwave background (CMB) radiation are described with remarkable accuracy by the six-parameter [Formula: see text]CDM cosmology. However, the key ingredients of this model, namely dark matter, dark energy and cosmic inflation are not understood at a fundamental level. It is, therefore, important to investigate tensions between the CMB and other cosmological probes. I will review aspects of tensions with direct measurements of the Hubble constant [Formula: see text], measurements of weak gravitational lensing, and the recent hints of evolving dark energy reported by the Dark Energy Spectroscopic Instrument (DESI) collaboration.This article is part of the discussion meeting issue 'Challenging the standard cosmological model'.

Cosmology from weak gravitational lensing has been limited by astrophysical uncertainties in baryonic feedback and intrinsic alignments. By calibrating these effects using external data, we recover non-linear information, achieving a 2

ABSTRACT Analyses of cosmic shear typically condense weak lensing information over a range of scales to a single cosmological parameter, $S_8$. This paper presents a method to extract more information from Stage IV cosmic shear measurements by directly reconstructing the matter power spectrum from linear to non-linear scales. We demonstrate that cosmic shear surveys will be sensitive to the shape of the matter power spectrum on non-linear scales. We show that it should be possible to distinguish between different models of baryonic feedback and we investigate the impact of intrinsic alignments and observational systematics on forecasted constraints. In addition to providing important information on galaxy formation, power spectrum reconstruction should provide a definitive answer to the question of whether weak lensing measurements of $S_8$ on linear scales are consistent with the Planck Lambda cold dark matter cosmology. In addition, power spectrum reconstruction may lead to new discoveries on the composition of the dark sector.

Observations of the cosmic microwave backgroundradiation are described to remarkable accuracy by the six-parameterLambda CDM cosmology. However, the key ingredients of this model, namely dark matter, dark energy and cosmic inflation are not understood at a fundamental level. It is therefore important to investigate tensions between the CMB and other cosmological probes. I will review aspects of tensions with direct measurements of the Hubble constant H_0, measurements of weak gravitational lensing, and the recent hints of evolving dark energy reported by the Dark Energy Spectroscopic Instrument (DESI) collaboration.

Axion-like early dark energy (EDE) as an extension to $\Lambda$CDM has been proposed as a possible solution to the 'Hubble tension'. We revisit this model using a new cosmic microwave background (CMB) temperature and polarization likelihood constructed from the {\it Planck} NPIPE data release. In a Bayesian analysis, we find that the maximum fractional contribution of EDE to the total energy density is $f_{\rm EDE} < 0.061$ (without SH0ES) over the redshift range $z\in[10^3,10^4]$ and that the Hubble constant is constrained to lie within the range $ 66.9 < H_0 < 69.5$ km/s/Mpc (both at 95 \% C.L.). The data therefore favour a model close to $\Lambda$CDM, leaving a residual tension of $3.7\sigma$ with the SH$0$ES Cepheid-based measurement of $H_0$. A comparison with the likelihood profile shows that our conclusions are robust to prior-volume effects. Our new CMB likelihood provides no evidence in favour of a significant EDE component.

George Efstathiou, recipient of the 2022 RAS Gold Medal in Astronomy, discusses the paradigm shifts that have led to the LCDM cosmology

We present constraints on primordial B modes from large angular scale cosmic microwave background polarisation anisotropies measured with the Planck satellite. To remove Galactic polarised foregrounds, we use a Bayesian parametric component separation method, modelling synchrotron radiation as a power law and thermal dust emission as a modified blackbody. This method propagates uncertainties from the foreground cleaning into the noise covariance matrices of the maps. We construct two likelihoods: (i) a semi-analytical cross-spectrum-based likelihood-approximation scheme (momento) and (ii) an exact polarisation-only pixel-based likelihood (pixlike). Since momento is based on cross-spectra it is statistically less powerful than pixlike, but is less sensitive to systematic errors correlated across frequencies. Both likelihoods give a tensor-to-scalar ratio, r, that is consistent with zero from low multipole (2 <= ell < 30) Planck polarisation data. From full-mission maps we obtain r_0.05<0.274, at 95 per cent confidence, at a pivot scale of k = 0.05 Mpc^-1, using pixlike. momento gives a qualitatively similar but weaker 95 per cent confidence limit of r_0.05<0.408.

Weak galaxy lensing surveys have consistently reported low values of the $S_8$ parameter compared to the $\textit{Planck}\ \Lambda\rm{CDM}$ cosmology. Amon & Efstathiou (2022) used KiDS-1000 cosmic shear measurements to propose that this tension can be reconciled if the matter fluctuation spectrum is suppressed more strongly on non-linear scales than assumed in state-of-the-art hydrodynamical simulations. In this paper, we investigate cosmic shear data from the Dark Energy Survey (DES) Year 3. The non-linear suppression of the matter power spectrum required to resolve the $S_8$ tension between DES and the $\textit{Planck}\ \Lambda\rm{CDM}$ model is not as strong as inferred using KiDS data, but is still more extreme than predictions from recent numerical simulations. An alternative possibility is that non-standard dark matter contributes to the required suppression. We investigate the redshift and scale dependence of the suppression of the matter power spectrum. If our proposed explanation of the $S_8$ tension is correct, the required suppression must extend into the mildly non-linear regime to wavenumbers $k\sim 0.2 h {\rm Mpc}^{-1}$. In addition, all measures of $S_8$ using linear scales should agree with the $\textit{Planck}\ \Lambda\rm{CDM}$ cosmology, an expectation that will be testable to high precision in the near future.

ABSTRACT We present a Bayesian parametric component separation method for polarized microwave sky maps. We solve jointly for the primary cosmic microwave background (CMB) signal and the main Galactic polarized foreground components. For the latter, we consider electron-synchrotron radiation and thermal dust emission, modelled in frequency as a power law and a modified blackbody, respectively. We account for inter-pixel correlations in the noise covariance matrices of the input maps and introduce a spatial correlation length in the prior matrices for the spectral indices β. We apply our method to low-resolution polarized Planck 2018 Low and High Frequency Instrument (LFI/HFI) data, including the SRoll2 re-processing of HFI data. We find evidence for spatial variation of the synchrotron spectral index, and no evidence for depolarization of dust. Using the HFI SRoll2 maps, and applying wide priors on the spectral indices, we find a mean polarized synchrotron spectral index over the unmasked sky of $\bar{\beta }_{\rm sync}=-2.83\pm 0.62$. For polarized thermal dust emission, we obtain $\bar{\beta }_{\rm dust}=1.43\pm 0.24$. Using our recovered CMB maps and associated uncertainties, we constrain the optical depth to reionization, τ, using a cross-spectrum-based likelihood-approximation scheme (momento) to be τ = 0.0598 ± 0.0059. We confirm our findings using a pixel-based likelihood (pixLike). In both cases, we obtain a result that is consistent with that found by subtracting spatially uniform foreground templates. While the latter method is sufficient for current polarization data from Planck, next-generation space-borne CMB experiments will need more powerful schemes such as the one presented here.

We present angular power spectra and cosmological parameter constraints derived from the Planck PR4 ( NPIPE ) maps of the Cosmic Microwave Background. NPIPE , released by the Planck Collaboration in 2020, is a new processing pipeline for producing calibrated frequency maps from Planck data. We have created new versions of the CamSpec likelihood using these maps and applied them to constrain Λ CDM and single-parameter extensions. We find excellent consistency between NPIPE and the Planck 2018 maps at the parameter level, showing that the Planck cosmology is robust to substantial changes in the mapmaking. The lower noise of NPIPE leads to ~10% tighter constraints, and we see both smaller error bars and a shift toward the Λ CDM values for beyond- Λ CDM parameters including Ω 𝐾 and 𝐴 𝐿 .

Weak galaxy lensing surveys have consistently reported a lower amplitude for the matter fluctuation spectrum, as measured by the S8 parameter, than expected in the ΛCDM cosmology favoured by Planck. However, the expansion history follows the predictions of the Planck ΛCDM cosmology to high accuracy, as do measurements of lensing of the cosmic microwave background anisotropies. Redshift space distortion measurements also appear to be consistent with Planck ΛCDM. In this paper, we argue that these observations can be reconciled with the Planck ΛCDM cosmology if the matter power spectrum is suppressed more strongly on non-linear scales than assumed in analyses of weak galaxy lensing. We demonstrate this point by fitting a one-parameter model, characterizing a suppression of the non-linear power spectrum, to the KiDS-1000 weak lensing measurements. Such a suppression could be attributed to new properties of the dark matter that affect non-linear scales, or to a response of the matter fluctuations to baryonic feedback processes that are stronger than expected from recent cosmological simulations. Our proposed explanation can be tested using measurements of the amplitude of the matter fluctuation spectrum on linear scales, in particular via high precision redshift space distortion measurements from forthcoming galaxy and quasar redshift surveys.

The polarized thermal emission from diffuse Galactic dust is the main foreground present in measurements of the polarization of the cosmic microwave background (CMB) at frequencies above 100 GHz. In this paper we exploit the uniqueness of the Planck HFI polarization data from 100 to 353 GHz to measure the polarized dust angular power spectra CEE ` and C BB ` over the multipole range 40 < ` < 600 well away from the Galactic plane. These measurements will bring new insights into interstellar dust physics and allow a precise determination of the level of contamination for CMB polarization experiments. Despite the non-Gaussian and anisotropic nature of Galactic dust, we show that general statistical properties of the emission can be characterized accurately over large fractions of the sky using angular power spectra. The polarization power spectra of the dust are well described by power laws in multipole, C` ∝ `, with exponents αEE,BB = −2.42± 0.02. The amplitudes of the polarization power spectra vary with the average brightness in a way similar to the intensity power spectra. The frequency dependence of the dust polarization spectra is consistent with modified blackbody emission with βd = 1.59 and Td = 19.6 K down to the lowest Planck HFI frequencies. We find a systematic difference between the amplitudes of the Galactic Band E-modes, CBB ` /C EE ` = 0.5. We verify that these general properties are preserved towards high Galactic latitudes with low dust column densities. We show that even in the faintest dust-emitting regions there are no “clean” windows in the sky where primordial CMB B-mode polarization measurements could be made without subtraction of foreground emission. Finally, we investigate the level of dust polarization in the specific field recently targeted by the BICEP2 experiment. Extrapolation of the Planck 353 GHz data to 150 GHz gives a dust powerDBB ` ≡ `(`+ 1)CBB ` /(2π) of 1.32× 10−2 μKCMB over the multipole range of the primordial recombination bump (40 < ` < 120); the statistical uncertainty is ±0.29 × 10−2 μKCMB and there is an additional uncertainty (+0.28,−0.24) × 10−2 μKCMB from the extrapolation. This level is the same magnitude as reported by BICEP2 over this ` range, which highlights the need for assessment of the polarized dust signal even in the cleanest windows of the sky.

This paper investigates whether changes to late time physics can resolve the ‘Hubble tension’. It is argued that many of the claims in the literature favouring such solutions are caused by a misunderstanding of how distance ladder measurements actually work and, in particular, by the inappropriate use of a distance ladder H0 prior. A dynamics-free inverse distance ladder shows that changes to late time physics are strongly constrained observationally and cannot resolve the discrepancy between the SH0ES data and the base ΛCDM cosmology inferred from Planck. We propose a statistically rigorous scheme to replace the use of H0 priors.

This paper presents a detailed description of the CamSpec likelihood which has been used to analyse Planck temperature and polarization maps of the cosmic microwave background since the first Planck data release. We have created a number of likelihoods using a range of Galactic sky masks and different methods of temperature foreground cleaning. Our most powerful likelihood uses 80 percent of the sky in temperature and polarization. Our results show that the six-parameter LCDM cosmology provides an excellent fit to the Planck data. There is no evidence for statistically significant internal tensions in the Planck TT, TE and EE spectra computed for different frequency combinations. We present evidence that the tendencies for the Planck temperature power spectra to favour a lensing amplitude A_L>1 and positive spatial curvature are caused by statistical fluctuations in the temperature power spectra. Using our statistically most powerful likelihood, we find that the A_L parameter differs from unity at no more than the 2.2 sigma level. We find no evidence for anomalous shifts in cosmological parameters with multipole range. In fact, we show that the combined TTTEEE likelihood over the restricted multipole range 2-800 gives cosmological parameters for the base LCDM cosmology that are very close to those derived from the full multipole range 2-2500. We present revised constraints on a few extensions of the base LCDM cosmology, focussing on the sum of neutrino masses, number of relativistic species and the tensor-scalar ratio. The results presented here show that the Planck data are remarkably consistent between detector-sets, frequencies and sky area. We find no evidence in our analysis that cosmological parameters determined from the CamSpec likelihood are affected to any significant degree by systematic errors in the Planck data (abridged).

This paper explores methods for constructing low multipole temperature and polarization likelihoods from maps of the cosmic microwave background anisotropies that have complex noise properties and partial sky coverage. We use Planck 2018 High Frequency Instrument (HFI) and updated SRoll2 temperature and polarization maps to test our methods. We present three likelihood approximations based on quadratic cross spectrum estimators: (i) a variant of the simulation-based likelihood (SimBaL) techniques used in the Planck legacy papers to produce a low multipole EE likelihood; (ii) a semi-analytical likelihood approximation (momento) based on the principle of maximum entropy; (iii) a density-estimation ‘likelihood-free’ scheme (delfi). Approaches (ii) and (iii) can be generalized to produce low multipole joint temperature-polarization (TTTEEE) likelihoods. We present extensive tests of these methods on simulations with realistic correlated noise. We then analyse the Planck data and confirm the robustness of our method and likelihoods on multiple inter- and intra-frequency detector set combinations of SRoll2 maps. The three likelihood techniques give consistent results and support a low value of the optical depth to reoinization, τ, from the HFI. Our best estimate of τ comes from combining the low multipole SRoll2momento (TTTEEE) likelihood with the CamSpec high multipole likelihood and is $\tau = 0.0627^{+0.0050}_{-0.0058}$. This is consistent with the SRoll2 team’s determination of τ, though slightly higher by ∼0.5σ, mainly because of our joint treatment of temperature and polarization.