Cluster counts

Abstract

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].