Amplitude Of Matter Fluctuations Research Articles

Accurate Measurement of the Lensing Magnification by BOSS CMASS Galaxies and Its Implications for Cosmology and Dark Matter

Magnification serves as an independent and complementary gravitational lensing measurement to shear. We develop a novel method to achieve an accurate and robust magnification measurement around BOSS CMASS galaxies across physical scales of 0.016h −1 Mpc < r p < 10h −1 Mpc. We first measure the excess total flux density δ M of the source galaxies in the deep DECaLS photometric catalog that are lensed by CMASS galaxies. We convert δ M to magnification μ by establishing the δ μ–δ M relation using a deeper photometric sample. By comparing magnification measurements in three optical bands (grz), we constrain the dust attenuation curve and its radial distribution, discovering a steep attenuation curve in the circumgalactic medium of CMASS galaxies. We further compare dust-corrected magnification measurements to model predictions from high-resolution dark matter-only (DMO) simulations in Wilkinson Microwave Anisotropy Probe (WMAP) and Planck cosmologies, as well as the hydrodynamic simulation TNG300-1, using precise galaxy–halo connections from the Photometric objects Around Cosmic webs method and the accurate ray-tracing algorithm P3MLens. For r p > 70h −1 kpc, our magnification measurements are in good agreement with both WMAP and Planck cosmologies, resulting in an estimation of the matter fluctuation amplitude of S 8 = 0.816 ± 0.024. However, at r p < 70h −1 kpc, we observe an excess magnification signal, which is higher than the DMO model in Planck cosmology at 2.8σ and would be exacerbated if significant baryon feedback is included. Implications of the potential small scale discrepancy for the nature of dark matter and for the processes governing galaxy formation are discussed.

Cosmological constraints from the eBOSS Lyman-α forest using the PRIYA simulations

We present new cosmological parameter constraints from the eBOSS Lyman-α forest survey. We use a new theoretical model and likelihood based on the PRIYA simulation suite. PRIYA is the first suite to resolve the Lyman-α forest in a (120 Mpc/h)3 volume, using a multi-fidelity emulation technique. We use PRIYA to predict Lyman-α forest observables with ≲ 1% interpolation error over an 11 dimensional (9 simulated, 2 in post-processing) parameter space. We identify an internal tension within the flux power spectrum data. Once the discrepant data is removed, we find the primeval scalar spectral index measured at a pivot scale of k 0 = 0.78 Mpc-1 to be nP = 1.009+0.027 -0.018 at 68% confidence. This measurement from the Lyman-α forest flux power spectrum alone is in reasonable agreement with Planck, and in tension with earlier eBOSS analyses. The amplitude of matter fluctuations is σ 8 = 0.733+0.026 -0.029 at 68% confidence, in agreement with Dark Energy Survey weak lensing measurements and other small-scale structure probes and in tension with CMB measurements from Planck and ACT. The effective optical depth to Lyman-α photons from our pipeline is in good agreement with earlier high resolution measurements. We find a linear power at z = 3 and k = 0.009 s/km of Δ2 L = 0.302+0.024 -0.027 with a slope n eff = -2.264+0.026 -0.018. Our flux power spectrum only chains prefer a low level of heating during helium reionization. When we add IGM temperature data we find nP = 0.983 ± 0.020 and σ 8 = 0.703+0.023 -0.027. Our chains prefer an early and long helium reionization event, as suggested by measurements from the helium Lyman-α forest. In the near future we will use our pipeline to infer cosmological parameters from the DESI Lyman-α data.

Growth history and quasar bias evolution at z < 3 from Quaia

We make use of the Gaia-unWISE quasar catalogue, Quaia, to constrain the growth history out to high redshifts from the clustering of quasars and their cross-correlation with maps of the Cosmic Microwave Background (CMB) lensing convergence. Considering three tomographic bins, centred at redshifts z̅i = [0.69, 1.59, 2.72], we reconstruct the evolution of the amplitude of matter fluctuations σ 8(z) over the last ∼ 12 billion years of cosmic history. In particular, we make one of the highest-redshift measurements of σ 8 (σ 8(z = 2.72) = 0.22 ± 0.06), finding it to be in good agreement (at the ∼ 1σ level) with the value predicted by ΛCDM using CMB data from Planck. We also used the data to study the evolution of the linear quasar bias for this sample, finding values similar to those of other quasar samples, although with a less steep evolution at high redshifts. Finally, we study the potential impact of foreground contamination in the CMB lensing maps and, although we find evidence of contamination in cross-correlations at z ∼ 1.7 we are not able to clearly pinpoint its origin as being Galactic or extragalactic. Nevertheless, we determine that the impact of this contamination on our results is negligible.

The Atacama Cosmology Telescope: Cosmology from Cross-correlations of unWISE Galaxies and ACT DR6 CMB Lensing

We present tomographic measurements of structure growth using cross-correlations of Atacama Cosmology Telescope (ACT) DR6 and Planck cosmic microwave background (CMB) lensing maps with the unWISE Blue and Green galaxy samples, which span the redshift ranges 0.2 ≲ z ≲ 1.1 and 0.3 ≲ z ≲ 1.8, respectively. We improve on prior unWISE cross-correlations not just by making use of the new, high-precision ACT DR6 lensing maps, but also by including additional spectroscopic data for redshift calibration and by analyzing our measurements with a more flexible theoretical model. We determine the amplitude of matter fluctuations at low redshifts (z ≃ 0.2–1.6), finding S8≡σ8(Ωm/0.3)0.5=0.813±0.021 using the ACT cross-correlation alone and S 8 = 0.810 ± 0.015 with a combination of Planck and ACT cross-correlations; these measurements are fully consistent with the predictions from primary CMB measurements assuming standard structure growth. The addition of baryon acoustic oscillation data breaks the degeneracy between σ 8 and Ω m , allowing us to measure σ 8 = 0.813 ± 0.020 from the cross-correlation of unWISE with ACT and σ 8 = 0.813 ± 0.015 from the combination of cross-correlations with ACT and Planck. These results also agree with the expectations from primary CMB extrapolations in ΛCDM cosmology; the consistency of σ 8 derived from our two redshift samples at z ∼ 0.6 and 1.1 provides a further check of our cosmological model. Our results suggest that structure formation on linear scales is well described by ΛCDM even down to low redshifts z ≲ 1.

Using the Kaniadakis horizon entropy in the presence of neutrinos to alleviate the Hubble and S8\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ S_{8} $$\\end{document} tensions

The H0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H_{0}$$\\end{document} tension stands as a prominent challenge in cosmology, serving as a primary driver for exploring alternative models of dark energy. Another tension arises from measurements of the S8\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ S_{8} $$\\end{document} parameter, which is characterize the amplitude of matter fluctuations in the universe. In this study, we address the alleviation of both the Hubble tension and S8\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ S_{8} $$\\end{document} tension by incorporating Kaniadakis horizon entropy. We investigate two scenarios to explore the impact of this entropy on cosmological parameters. In the first scenario, utilizing modified Friedmann equations through Kaniadakis entropy, we estimate the values of H0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H_{0}$$\\end{document} and S8\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ S_{8} $$\\end{document}. In the subsequent scenario, we introduce the neutrino term and assess its effect on mitigating the Hubble and S8\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ S_{8} $$\\end{document} tensions. Our findings reveal that when considering the first scenario, the results closely align with Planck’s 2018 outcomes for Hubble and S8\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ S_{8} $$\\end{document} tensions. Moreover, with the inclusion of neutrinos, these tensions are alleviated to approximately 2σ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma $$\\end{document}, and the S8\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ S_{8} $$\\end{document} value is in full agreement with the results from the KiDS and DES survey. Furthermore, we impose a constraint on the parameter K in each scenario. Our analysis yields K=0.12±0.41\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$K = 0.12\\pm 0.41$$\\end{document} for Kaniadakis entropy without neutrinos and K=0.39±0.4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$K = 0.39\\pm 0.4$$\\end{document} for the combined dataset considering Kaniadakis entropy in the presence of neutrinos. We demonstrate that the value of K may be affected by neutrino mass, which can cause energy transfer between different parts of the universe and alter the Hubble parameter value.

Growth of structures using redshift space distortion in f(T) cosmology

ABSTRACT Cosmology faces a pressing challenge with the Hubble constant (H0) tension, where the locally measured rate of the Universe’s expansion does not align with predictions from the cosmic microwave background calibrated with lambda-cold dark matter model. Simultaneously, there is a growing tension involving the weighted amplitude of matter fluctuations, known as S8,0 tension. Resolving both tensions within one framework would boost confidence in any one particular model. In this work, we analyse constraints in f(T) gravity, a framework that shows promise in shedding light on cosmic evolution. We thoroughly examine prominent f(T) gravity models using a combination of data sources, including pantheon+ (SN), cosmic chronometers, baryonic acoustic oscillations, and redshift space distortion data. We use these models to derive a spectrum of H0 and S8,0 values, aiming to gauge their ability to provide insights into, and potentially address, the challenges posed by the H0 and S8,0 tensions.

GEO-FPT: a model of the galaxy bispectrum at mildly non-linear scales

We present GEO-FPT (Geometric Fitted Perturbation Theory), a new model for the galaxy bispectrum anisotropic signal in redshift space, with functional form rooted in perturbation theory. It also models the dependence of the bispectrum with the geometric properties of the triangles in Fourier space, and has a broader regime of validity thanstate-of-the-art theoretical models based on perturbation theory. We calibrate the free parameters of this model using high-resolution dark matter simulations and perform stringent tests to show that GEO-FPTdescribes the galaxy bispectrum accurately up to scales of k ≃ 0.12hMpc-1 for different cosmological models, as well as for biased tracers of the dark matter field, considering a survey volume of 100 (Gpc h-1)3. In particular, a joint analysis ofthe power spectrum and bispectrum anisotropic signals, taking into account their full covariance matrix, reveals that therelevant physical quantities —the BAO peak position (along and across the line-of-sight), and the growth of structure parameters times the amplitude of dark matter fluctuations, fσ 8 — are recovered in an unbiased way, with an accuracy better than 0.4% and 2% respectively (which is our 2σ statistical limit of the systematic error estimate).In addition, the bispectrum signal breaks the fσ 8 degeneracy without detectable bias: f and σ 8 are recovered with better than 2.7% and 3.8% accuracy respectively (which is our 2σ statistical limit of the systematic error estimate).GEO-FPT boosts the applicability of the bispectrum signal of galaxy surveys beyond the current limitation of k ≲ 0.08hMpc-1 and makes the bispectrum a key statistic to unlock the information content from the mildly non-linear regime in the on-going and forthcoming galaxy redshift surveys.

Constraining cosmology with the Gaia-unWISE Quasar Catalog and CMB lensing: structure growth

We study the angular clustering of Quaia, a Gaia- and unWISE-based catalog of over a million quasars with an exceptionally well-defined selection function. With it, we derive cosmology constraints from the amplitude and growth of structure across cosmic time. We divide the sample into two redshift bins, centered at z = 1.0 and z = 2.1, and measure both overdensity auto-correlations and cross-correlations with maps of the Cosmic Microwave Background convergence measured by Planck. From these data, and including a prior from measurements of the baryon acoustic oscillations scale, we place constraints on the amplitude of the matter power spectrum σ 8 = 0.766 ± 0.034, and on the matter density parameter Ω m = 0.343+0.017 -0.019. These measurements are in reasonable agreement with Planck at the ∼ 1.4σ level, and are found to be robust with respect to observational and theoretical uncertainties. We find that our slightly lower value of σ 8 is driven by the higher-redshift sample, which favours a low amplitude of matter fluctuations. We present plausible arguments showing that this could be driven by contamination of the CMB lensing map by high-redshift extragalactic foregrounds, which should also affect other cross-correlations with tracers of large-scale structure beyond z ∼ 1.5. Our constraints are competitive with those from state-of-the-art 3×2-point analyses, but arise from a range of scales and redshifts that is highly complementary to those covered by cosmic shear data and most galaxy clustering samples. This, coupled with the unprecedented combination of volume and redshift precision achieved by Quaia, allows us to break the usual degeneracy between Ω m and σ 8.

Rock ‘n’ roll solutions to the Hubble tension

Local measurements of the Hubble parameter are increasingly in tension with the value inferred from a ΛCDM fit to the cosmic microwave background (CMB) data. In this paper, we construct scenarios in which evolving scalar fields significantly ease this tension by adding energy to the Universe around recombination in a narrow redshift window. We identify solutions with scalar field potential V∝ϕ2n that have simple asymptotic behavior, both oscillatory (rocking) and rolling. These solutions consistently describe both the field evolution and its fluctuations without approximation. Our findings differ qualitatively from some of the existing literature, which rely upon a coarse-grained fluid description. Combining CMB data with low-redshift measurements, the best fit model has n=2 with a significantly higher value of the Hubble constant as compared to a ΛCDM fit to the same data. Future measurements of the late-time amplitude of matter fluctuations and of the reionization history could help distinguish these models from competing solutions.

Evidence for Suppression of Structure Growth in the Concordance Cosmological Model.

We present evidence for a suppressed growth rate of large-scale structure during the dark-energy-dominated era. Modeling the growth rate of perturbations with the "growth index" γ, we find that current cosmological data strongly prefer a higher growth index than the value γ=0.55 predicted by general relativity in a flat Lambda cold dark matter cosmology. Both the cosmic microwave background data from Planck and the large-scale structure data from weak lensing, galaxy clustering, and cosmic velocities separately favor growth suppression. When combined, they yield γ=0.633_{-0.024}^{+0.025}, excluding γ=0.55 at a statistical significance of 3.7σ. The combination of fσ_{8} and Planck measurements prefers an even higher growth index of γ=0.639_{-0.025}^{+0.024}, corresponding to a 4.2σ tension with the concordance model. In Planck data, the suppressed growth rate offsets the preference for nonzero curvature and fits the data equally well as the latter model. A higher γ leads to a higher matter fluctuation amplitude S_{8} inferred from galaxy clustering and weak lensing measurements, and a lower S_{8} from Planck data, effectively resolving the S_{8} tension.

The Dark Energy Survey Year 3 high-redshift sample: selection, characterization, and analysis of galaxy clustering

ABSTRACT The fiducial cosmological analyses of imaging surveys like DES typically probe the Universe at redshifts z &amp;lt; 1. We present the selection and characterization of high-redshift galaxy samples using DES Year 3 data, and the analysis of their galaxy clustering measurements. In particular, we use galaxies that are fainter than those used in the previous DES Year 3 analyses and a Bayesian redshift scheme to define three tomographic bins with mean redshifts around z ∼ 0.9, 1.2, and 1.5, which extend the redshift coverage of the fiducial DES Year 3 analysis. These samples contain a total of about 9 million galaxies, and their galaxy density is more than 2 times higher than those in the DES Year 3 fiducial case. We characterize the redshift uncertainties of the samples, including the usage of various spectroscopic and high-quality redshift samples, and we develop a machine-learning method to correct for correlations between galaxy density and survey observing conditions. The analysis of galaxy clustering measurements, with a total signal to noise S/N ∼ 70 after scale cuts, yields robust cosmological constraints on a combination of the fraction of matter in the Universe Ωm and the Hubble parameter h, $\Omega _m h = 0.195^{+0.023}_{-0.018}$, and 2–3 per cent measurements of the amplitude of the galaxy clustering signals, probing galaxy bias and the amplitude of matter fluctuations, bσ8. A companion paper (in preparation) will present the cross-correlations of these high-z samples with cosmic microwave background lensing from Planck and South Pole Telescope, and the cosmological analysis of those measurements in combination with the galaxy clustering presented in this work.

Consistent clustering and lensing of SDSS-III BOSS galaxies with an extended abundance matching formalism

ABSTRACT Several analyses have shown that Λ cold dark matter-based models cannot jointly describe the clustering (GC) and galaxy–galaxy lensing (GGL) of galaxies in the Sloan Digital Sky Survey-III (SDSS-III) Baryon Oscillation Spectroscopic Survey (BOSS), which is commonly known as the ‘lensing-is-low problem’. In this work, we show that an extension of Subhalo Abundance Matching, dubbed SHAMe, successfully solves this problem. First, we show that this model accurately reproduces the GC and GGL of a mock galaxy sample in the TNG300 hydrodynamic simulation with properties analogous to those of BOSS galaxies. Then, we switch our attention to observed BOSS galaxies at z = 0.31−0.43, and we attempt to reproduce their GC and GGL by evaluating SHAMe on two different simulations: one adopting best-fitting cosmological parameters from Planck and the other from weak gravitational lensing surveys (Low S8), where the amplitude of matter fluctuations is lower for the latter. We find excellent agreement between SHAMe predictions and observations for both cosmologies, indicating that the lensing-is-low problem originates from approximations in previous theoretical descriptions of the data. The main difference between SHAMe results in these cosmologies is the level of galaxy assembly bias, which is approximately 20 per cent and 10 per cent for Planck and Low S8, respectively. These results highlight the dangers of employing oversimplified models to analyse current large-scale structure data sets, and the need for realistic yet flexible descriptions of the galaxy–halo connection.

Cosmology in Minkowski space

Theoretical and observational challenges to standard cosmology such as the cosmological constant problem and tensions between cosmological model parameters inferred from different observations motivate the development and search of new physics. A less radical approach to venturing beyond the standard model is the simple mathematical reformulation of our theoretical frameworks underlying it. While leaving physical measurements unaffected, this can offer a reinterpretation and even solutions of these problems. In this spirit, metric transformations are performed here that cast our Universe into different geometries. Of particular interest thereby is the formulation of cosmology in Minkowski space. Rather than an expansion of space, spatial curvature, and small-scale inhomogeneities and anisotropies, this frame exhibits a variation of mass, length and time scales across spacetime. Alternatively, this may be interpreted as an evolution of fundamental constants. As applications of this reframed cosmological picture, the naturalness of the cosmological constant is reinspected and promising candidates of geometric origin are explored for dark matter, dark energy, inflation and baryogenesis. An immediate observation thereby is the apparent absence of the cosmological constant problem in the Minkowski frame. The formalism is also applied to identify new observable signatures of conformal inhomogeneities, which have been proposed as simultaneous solution of the observational tensions in the Hubble constant, the amplitude of matter fluctuations, and the gravitational lensing amplitude of cosmic microwave background anisotropies. These are found to enhance redshifts to distant galaxy clusters and introduce a mass bias with cluster masses inferred from gravitational lensing exceeding those inferred kinematically or dynamically.

Correction to: The matter fluctuation amplitude inferred from the weak lensing power spectrum and correlation function in CFHTLenS data

Correction to: The matter fluctuation amplitude inferred from the weak lensing power spectrum and correlation function in CFHTLenS data

Smoothing the [formula omitted] tension with a phantom dynamical dark energy model

The discrepancy between Planck data and direct measurements of the current expansion rate H0 and the matter fluctuation amplitude S8 has become one of the most intriguing puzzles in cosmology nowadays. The H0 tension has reached 5σ in the context of standard cosmology i.e ΛCDM. Therefore, explanations to this issue are mandatory to unveil its secrets. Despite its success, ΛCDM is unable to give a satisfying explanation to the tension problem. Unless some systematic errors are hidden in the observable measurements, physics beyond the standard model of cosmology must be advocated. In this perspective, we study a phantom dynamical dark energy model as an alternative to ΛCDM in order to explain the aforementioned issues. This phantom model is characterized by one extra parameter, Ωpdde, compared to ΛCDM. We obtain a strong positive correlation between H0 and Ωpdde, for all data combinations. Using Planck18 measurements together with BAO and Pantheon, we find that the H0 and the S8 tensions are 3.4σ and 2.75σ, respectively. By introducing a prior on the absolute magnitude, MB, of the SN Ia, the H0 tension decreases to 2.49σ with H0=69.7−0.86+0.83 km s−1 Mpc−1 and the S8 tension reaches the value 2.51σ with S8=0.82650.012+0.011.

Starlet higher order statistics for galaxy clustering and weak lensing

We present a first application to photometric galaxy clustering and weak lensing of wavelet-based multi-scale (beyond two points) summary statistics: starlet peak counts and starlet ℓ1-norm. Peak counts are the local maxima in the map, and ℓ1-norm is computed via the sum of the absolute values of the starlet (wavelet) decomposition coefficients of a map, providing a fast multi-scale calculation of the pixel distribution, encoding the information of all pixels in the map. We employ the cosmo-SLICS simulations sources and lens catalogues, and we compute wavelet-based non-Gaussian statistics in the context of combined probes and their potential when applied to the weak-lensing convergence maps and galaxy maps. We obtain forecasts on the matter density parameter Ωm, the reduced Hubble constant h, the matter fluctuation amplitude σ8, and the dark energy equation of state parameter w0. In our setting for this first application, we consider the two probes to be independent. We find that the starlet peaks and the ℓ1-norm represent interesting summary statistics that can improve the constraints with respect to the power spectrum, even in the case of photometric galaxy clustering and when the two probes are combined.

Cluster counts

Despite the success of the Lambda cold dark matter (ΛCDM) cosmological model, current estimations of the amplitude of matter fluctuations (σ8) show an appreciable difference between its value inferred from the cosmic microwave background (CMB) angular power spectrum (Cℓ) and those obtained from cluster counts. Neutrinos or a modification of the growth of structures had been previously investigated as the possible origin of this discrepancy. In this work we examine whether further extensions to the ΛCDM model could alleviate the tension. To this end, we derived constraints on the parameters subject to the discrepancy, using CMB Cℓ combined with cluster counts from the Sunyaev–Zel’dovich (SZ) sample with a free dark energy equation of state parameter, while allowing the cluster mass calibration parameter (1 − b) to vary. This latter is degenerate with σ8, which translates the discrepancy within the ΛCDM framework into one between (1 − b)∼0.6, corresponding to constraints on σ8 obtained from CMB, and (1 − b)∼0.8, the value adopted for the SZ sample calibration. We find that a constant w, when left free to vary along with large priors on the matter density ([0.1, 1.0]) and the Hubble parameters ([30, 200]), can reduce the discrepancy to less than 2σ for values far below its fiducial w = −1. However, such low values of w are not allowed when we add other probes like the baryonic acoustic oscillation (BAO) feature angular diameter distance measured in galaxy clustering surveys. We also found, when we allow to vary in addition to w a modification of the growth rate through the growth index γ, that the tension is alleviated, with the (1 − b) likelihood now centred around the Planck calibration value of ∼0.8. However, here again, combining CMB and cluster counts with geometrical distance probes restores the discrepancy, with the (1 − b) preferred value reverting back to the ΛCDM value of ∼0.6. The same situation is observed when introducing, along with w and γ, further extensions to ΛCDM (e.g., massive neutrinos), although these extensions reduce the tension to 2σ, even when combined with BAO datasets. We also explore other common extensions by comparing two cases: allowing a dynamical w following a CPL parametrisation in addition to a constant growth index, and when the growth index is expanded through a second parameter γ1 along with a constant w. In the former we reach the same conclusions as with the case of a constant w and γ, where the discrepancy was alleviated only if we do not constrain w by BAO, while in the latter case, we observe that introducing γ1 drives (1 − b) towards lower values that would instead increase the discrepancy on σ8. We conclude that none of these common extensions to ΛCDM is able to fix the discrepancy and a misdetermination of the calibration factor is the most preferred explanation. Finally, we investigate the effect on our posteriors from limiting the Hubble constant priors to the usual common adopted range of [30, 100].

Decaying warm dark matter revisited

Decaying dark matter models provide a physically motivated way of channeling energy between the matter and radiation sectors. In principle, this could affect the predicted value of the Hubble constant in such a way as to accommodate the discrepancies between CMB inferences and local measurements of the same. Here, we revisit the model of warm dark matter decaying non-relativistically to invisible radiation. In particular, we rederive the background and perturbation equations starting from a decaying neutrino model and describe a new, computationally efficient method of computing the decay product perturbations up to large multipoles. We conduct MCMC analyses to constrain all three model parameters, for the first time including the mass of the decaying species, and assess the ability of the model to alleviate the Hubble and σ 8 tensions, the latter being the discrepancy between the CMB and weak gravitational lensing constraints on the amplitude of matter fluctuations on an 8 h -1 Mpc-1 scale. We find that the model reduces the H 0 tension from ∼ 4σ to ∼ 3σ and neither alleviates nor worsens the S 8 ≡ σ 8 (Ω m /0.3)0.5 tension, ultimately showing only mild improvements with respect to ΛCDM. However, the values of the model-specific parameters favoured by data is found to be well within the regime of relativistic decays where inverse processes are important, rendering a conclusive evaluation of the decaying warm dark matter model open to future work.

Testing the ΛCDM paradigm with growth rate data and machine learning

The cosmological constant Λ and cold dark matter (CDM) model (ΛCDM) is one of the pillars of modern cosmology and is widely used as the de facto theoretical model by current and forthcoming surveys. As the nature of dark energy is very elusive, in order to avoid the problem of model bias, here we present a novel null test at the perturbation level that uses the growth of matter perturbation data in order to assess the concordance model. We analyze how accurate this null test can be reconstructed by using data from forthcoming surveys creating mock catalogs based on ΛCDM and three models that display a different evolution of the matter perturbations, namely a dark energy model with constant equation of state w (wCDM), the Hu & Sawicki and designer f(R) models, and we reconstruct them with a machine learning technique known as the Genetic Algorithms. We show that with future LSST-like mock data our consistency test will be able to rule out these viable cosmological models at more than 5σ, help to check for tensions in the data and alleviate the existing tension of the amplitude of matter fluctuations S 8 = σ 8 (Ωm,0/0.3)0.5.

Implications of the S8 tension for decaying dark matter with warm decay products

Recent weak lensing surveys have revealed that the direct measurement of the parameter combination $S_8\equiv\sigma_8(\Omega_m/0.3)^{0.5}$ -- where $\sigma_8$ is a measure of the amplitude of matter fluctuations on 8 $h^{-1}$Mpc scales -- is $\sim3\sigma$ discrepant with the value reconstructed from cosmic microwave background (CMB) data assuming the $\Lambda$CDM model. In this article, we show that it is possible to resolve the tension if dark matter (DM) decays with a lifetime of $\Gamma^{-1} \simeq 55 \ \text{Gyrs}$ into one massless and one massive product, and transfers a fraction $\varepsilon\simeq 0.7 \ \%$ of its rest mass energy to the massless component. The velocity-kick received by the massive daughter leads to a suppression of gravitational clustering below its free-streaming length, thereby reducing the $\sigma_8$ value as compared to that inferred from the standard $\Lambda$CDM model, in a similar fashion to massive neutrino and standard warm DM. Contrarily to the latter scenarios, the time-dependence of the power suppression and the free-streaming scale allows the 2-body decaying DM scenario to accommodate CMB, baryon acoustic oscillation, growth factor and un-calibrated supernova Ia data. We briefly discuss implications for DM model building, galactic small-scale structure problems and the recent Xenon-1T excess. Future experiments measuring the growth factor to high accuracy at $0\lesssim z\lesssim1$ can further test this scenario.