Cluster counts became a precision cosmological probe in the first decade of the 21st century, mostly through the analysis of X-ray cluster samples from ROSAT catalogues (Borgani et al.,2001; Reiprich and Böhringer, 2002; Seljak, 2002; Viana et al.,2002;
2004; Henry, 2004; Mantz et al., 2008; Vikhlinin et al.,2009;Henry et al.,2009;Mantz et al.,2010), but also thanks to optical analyses (Rozo et al., 2010). These works used widely different cluster samples and a range of observables such as the X-ray luminosity, the most commonly employed, the gas mass, YX (X-ray), and richness (optical). They
consistently found values of Ωm around 0.3 and of σ8 around 0.8, in agreement with
the constraints derived from CMB experiments such as WMAP (Hinshaw et al.,2013). This is a remarkable agreement given the huge redshift difference between galaxy clusters and the CMB, the very different physics that come into play in these two different cosmological probes, and the very different systematic effects to which they are sensitive.
Over the past 10 years there has been significant further progress in both X-ray (Mantz et al.,2015;Schellenberger and Reiprich,2017;Pacaud et al., 2018) and optical (Costanzi et al., 2019; Kirby et al., 2019) counts analyses, from which competitive cosmological constraints have been derived. These have been joined by the first generation of tSZ-based analyses (Benson et al., 2013; Hasselfield et al., 2013; Planck 2013 results XX, 2014; de Haan et al.,2016; Planck 2015 results XXIV,2016;Bocquet et al., 2019). An important contribution to this progress has come from the now- widespread use of weak-lensing masses to anchor the absolute cluster mass scale. As the analyses of the previous decade, these studies differ widely in their methodology and in the cluster samples and mass observables employed, and they are also sensitive to different systematic effects. Nonetheless, the cosmological constraints derived from them are in excellent agreement with each other and with constraints derived from other low-redshift cosmological probes, such as cosmic shear. There is also good agreement with the constraints derived from the Planck CMB assuming ΛCDM, except perhaps in one parameter, σ8. Indeed, recent low-redshift analyses, cluster counts included,
generally find constraints on σ8 that are somewhat lower than the Planck-derived one,
σ8 = 0.8111 ± 0.0060 (Planck 2018 TT,TE,EE+lowE+lensing results; Planck 2018
results VI 2018).
This situation is illustrated in Figure 1.11, which shows the constraints on σ8 at
Ωm= 0.3 derived from a number of recent cosmological analyses. The constraints from
cluster counts, which are classified into X-ray, SZ, and optical types, are shown in blue; those from cosmic shear, also a low-redshift probe, are shown in green for comparison; and the CMB-derived constraints are shown in red. Error bars denote 1 σ uncertainties. It can be seen how all the low-redshift constraints on σ8are in very good agreement with
each other. Moreover, as noted in Pratt et al. (2019), the empirical standard deviation of the cluster constraints around their empirical mean, shown as a light blue band, is
Fig. 1.11 Constraints on σ8 at Ωm = 0.3 from a number of recent studies. Constraints
from cluster counts (sometimes combined with gas fraction) are shown in blue, con- straints from cosmic shear are shown in green, and CMB-derived constraints are shown in red. Error bars denote 1 σ uncertainties. The light blue band corresponds to the standard deviation around the unweighted empirical mean of the seven independent cluster constraints, whereas the dark blue band corresponds to the empirical error on this unweighted mean. Figure credit: Pratt et al. 2019.
similar to the typical uncertainty of the individual cluster constraints, which indicates that uncertainties are well-understood and that confirmation bias is small. These low redshift constraints are also in good agreement with the constraint from WMAP, and, individually, with the much more precise constraint from Planck. However, the fact that all the cluster constraints, and indeed all the low-redshift constraints, except that from ACT (Hasselfield et al.,2013), are lower than the Planck constraint has attracted some attention in the community.
Unaccounted-for systematics in the less-robust low-redshift probes (as opposed to the better-understood CMB) are the most probable cause of this mild statistical discrepancy, at least from an Occam’s razor point of view. For cluster counts, some likely candidates are absolute calibration errors of X-ray instruments, which can also affect X-ray-calibrated SZ analyses (temperatures measured by XMM-Newton, for instance, have been found to be systematically higher than those measured by Chandra; see, e.g.,Schellenberger et al. 2015); relevant unaccounted-for relativistic tSZ corrections (e.g., Remazeilles et al. 2019); errors in the modelling of the ICM (e.g.,Ruppin et al.
2019); and badly-understood completeness, due to clusters that should be detected being missed by detection algorithms (e.g., Xu et al. 2018). These systematics can be generally encapsulated as biases in the mass calibration of the cluster observables, which are in turn sometimes accounted for by an overall ‘hydrostatic mass bias’ parameter. Some recent studies have found this bias to be too large to be consistent with the range that is expected from deviations from hydrostatic equilibrium and non-thermal pressure support as observed in hydrodynamical simulations (e.g., Planck 2015 results XXIV 2016, where a bias of about 40 % is required to reconcile fully the Planck SZ counts with the Planck CMB; see also Chapter 3). This can therefore hint at further unaccounted-for systematics.
Alternatively, this apparent discrepancy could be the first sign of some unknown new physics that suppresses structure formation at low redshifts. This late-time suppression could be potentially achieved with, e.g., dark energy with w > −1, as it starts dominating earlier and therefore structure growth stalls earlier, and with more massive neutrinos, as they erase inhomogeneities through free-streaming. These proposed extensions to ΛCDM, however, seem not to be favoured by current data (see, e.g., Planck 2015 results XXIV 2016 and Bolliet et al. 2019).