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In recent years, the amplitude of matter fluctuations inferred from low-redshift probes has been found to be generally lower than the value derived from CMB observations in the $Lambda$CDM model. This tension has been exemplified by Sunyaev-Zeldovich and X-ray cluster counts which, when using their Planck standard cluster mass calibration, yield a value of $sigma_8$ , appreciably lower than estimations based on the latest Planck CMB measurements. In this work we examine whether non-minimal neutrino masses can alleviate this tension substantially. We used the cluster X-ray temperature distribution function derived from a flux-limited sample of local X-ray clusters, combined with Planck CMB measurements. These datasets were compared to $Lambda$CDM predictions based on recent mass function, adapted to account for the effects of massive neutrinos. Treating the clusters mass calibration as a free parameter, we examined whether the data favours neutrino masses appreciably higher than the minimal 0.06 eV value. Using Markov chain Monte Carlo methods, we found no significant correlation between the mass calibration of clusters and the sum of neutrino masses, meaning that massive neutrinos do not noticeably alleviate the above-mentioned Planck CMB--clusters tension. The addition of other datasets (BAO and Ly-$alpha$) reinforces those conclusions. As an alternative possible solution to the tension, we introduced a simple, phenomenological modification of gravity by letting the growth index $gamma$ vary as an additional free parameter. We find that the cluster mass calibration is robustly correlated with the $gamma$ parameter, insensitively to the presence of massive neutrinos or/and additional data used. We conclude that the standard Planck mass calibration of clusters, if consolidated, would represent evidence for new physics beyond $Lambda$CDM with massive neutrinos.
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The mass of galaxy clusters can be inferred from the temperature of their X-ray emitting gas, $T_{mathrm{X}}$. Their masses may be underestimated if it is assumed that the gas is in hydrostatic equilibrium, by an amount $b^{mathrm{hyd}}sim(20pm10)$ % suggested by simulations. We have previously found consistency between a sample of observed textit{Chandra} X-ray masses and independent weak lensing measurements. Unfortunately, uncertainties in the instrumental calibration of {em Chandra} and {em XMM-Newton} observatories mean that they measure different temperatures for the same gas. In this paper, we translate that relative instrumental bias into mass bias, and infer that textit{XMM-Newton} masses of $sim 10^{14},mbox{M}_{odot}$ ($> 5cdot 10^{14} mbox{M}_{odot}$) clusters are unbiased ($sim 35$ % lower) compared to WL masses. For massive clusters, textit{Chandra}s calibration may thus be more accurate. The opposite appears to be true at the low mass end. We observe the mass bias to increase with cluster mass, but presence of Eddington bias precludes firm conclusions at this stage. Nevertheless, the systematic textit{Chandra} -- textit{XMM-Newton} difference is important because {em Planck}s detections of massive clusters via the Sunyaev-Zeldovich (SZ) effect are calibrated via {em XMM-Newton} observations. The number of detected SZ clusters are inconsistent with {em Planck}s cosmological measurements of the primary Cosmic Microwave Background (CMB). Given the textit{Planck} cluster masses, if an (unlikely) uncorrected $sim 20$ % calibration bias existed, this tension would be eased, but not resolved.
We present high signal-to-noise galaxy-galaxy lensing measurements of the BOSS CMASS sample using 250 square degrees of weak lensing data from CFHTLenS and CS82. We compare this signal with predictions from mock catalogs trained to match observables including the stellar mass function and the projected and two dimensional clustering of CMASS. We show that the clustering of CMASS, together with standard models of the galaxy-halo connection, robustly predicts a lensing signal that is 20-40% larger than observed. Detailed tests show that our results are robust to a variety of systematic effects. Lowering the value of $S_{rm 8}=sigma_{rm 8} sqrt{Omega_{rm m}/0.3}$ compared to Planck2015 reconciles the lensing with clustering. However, given the scale of our measurement ($r<10$ $h^{-1}$ Mpc), other effects may also be at play and need to be taken into consideration. We explore the impact of baryon physics, assembly bias, massive neutrinos, and modifications to general relativity on $DeltaSigma$ and show that several of these effects may be non-negligible given the precision of our measurement. Disentangling cosmological effects from the details of the galaxy-halo connection, the effects of baryons, and massive neutrinos, is the next challenge facing joint lensing and clustering analyses. This is especially true in the context of large galaxy samples from Baryon Acoustic Oscillation surveys with precise measurements but complex selection functions.
Persistent tension between low-redshift observations and the Cosmic Microwave Background radiation (CMB), in terms of two fundamental distance scales set by the sound horizon $r_d$ and the Hubble constant $H_0$, suggests new physics beyond the Standard Model or residual systematics. We examine recently updated distance calibrations from Cepheids, gravitational lensing time-delay observations, and the Tip of the Red Giant Branch. Calibrating the Baryon Acoustic Oscillations (BAO) and Type Ia supernovae with combinations of the distance indicators, we obtain a joint and self-consistent measurement of $H_0$ and $r_d$ at low redshift, independent of cosmological models and CMB inference. In an attempt to alleviate the tension between late-time and CMB-based measurements, we consider four extensions of the standard $Lambda$CDM model. The sound horizon from our different measurements is $r_d=(137pm3^{stat.}pm2^{syst.})$~Mpc. Depending on the adopted distance indicators, the $combined$ tension in $H_0$ and $r_d$ ranges between 2.3 and 5.1 $sigma$. We find that modifications of $Lambda$CDM that change the physics after recombination fail to solve the problem, for the reason that they only resolve the tension in $H_0$, while the tension in $r_d$ remains unchanged. Pre-recombination extensions (with early dark energy or the effective number of neutrinos $rm{N}_{rm{eff}}=3.24 pm 0.16$) are allowed by the data, unless the calibration from Cepheids is included. Results from time-delay lenses are consistent with those from distance-ladder calibrations and point to a discrepancy between absolute distance scales measured from the CMB (assuming the standard cosmological model) and late-time observations. New proposals to resolve this tension should be examined with respect to reconciling not only the Hubble constant but also the sound horizon derived from the CMB and other cosmological probes.
Cluster number counts can constrain the properties of dark energy if and only if the evolution in the relationship between observable quantities and the cluster mass can be calibrated. Next generation surveys with ~10000 clusters will have sufficient statistics to enable some degree of self-calibration. The excess variance of counts due to the clustering of clusters provides such an opportunity and can be measured from the survey without additional observational cost. It can minimize the degradation in dark energy constraints due to an unknown power law evolution in the mass-observable relation improving constraints on the dark energy equation of state by a factor of 2 or more to sigma(w)=0.06 for a deep 4000 deg2 survey.
The $Lambda$CDM concordance model is very successful at describing our Universe with high accuracy and few parameters. Despite its successes, a few tensions persist; most notably, the best-fit $Lambda$CDM model, as derived from the Planck CMB data, largely overpredicts the abundance of SZ clusters when using their standard mass calibration. Whether this is a sign of an incorrect calibration or the need for new physics remains a matter of debate. Here we examined two simple extensions of the standard model and their ability to release this tension: massive neutrinos and a simple modified gravity model via a non-standard growth index $gamma$. We used both the Planck CMB and SZ cluster counts as datasets, with or without local X-ray clusters. In the case of massive neutrinos, the SZ calibration $(1-b)$ is constrained to $0.59^{+0.03}_{-0.04}$ (68%), more than 5$sigma$ away from its standard value $sim0.8$. We found little correlation between $sum m_ u$ and $(1-b)$, corroborating previous conclusions derived from X-ray clusters; massive neutrinos do not alleviate the cluster-CMB tension. With our simple $gamma$ model, we found a large correlation between calibration and growth index but contrary to local X-ray clusters, SZ clusters are able to break the degeneracy between the two thanks to their extended $z$ range. The calibration $(1-b)$ was then constrained to $0.60^{+0.05}_{-0.07}$, leading to an interesting constraint on $gamma=0.60pm 0.13$. When both massive neutrinos and modified gravity were allowed, preferred values remained centred on standard $Lambda$CDM values, but $(1-b)sim0.8$ was allowed (though only at the $2sigma$ level) provided $sum m_ usim0.34 $ eV and $gammasim0.8$. We conclude that massive neutrinos do not relieve the cluster-CMB tension and that a calibration close to the standard value $0.8$ would call for new physics in the gravitational sector.
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