2021ApJ...911...82C

In recent years, the availability of large, complete cluster samples has enabled numerous cosmological parameter inference analyses using cluster number counts. These have provided constraints on the cosmic matter density Ω_m and the amplitude of matter density fluctuations σ₈ alternative to that obtained from other standard probes. However, systematics uncertainties, such as the mass calibration bias and selection effects, may still significantly affect these data analyses. Hence, it is timely to explore other proxies of galaxy cluster cosmology that can provide cosmological constraints complementary to those obtained from cluster number counts. Here we use measurements of the cluster sparsity from weak-lensing mass estimates of the LC²-single and HSC-XXL cluster catalogs to infer constraints on a flat ΛCDM model. The cluster sparsity has the advantage of being insensitive to selection and mass calibration bias. On the other hand, it primarily constrains a degenerate combination of Ω_m and σ₈ (along approximately constant curves of S₈=σ₈sqrt(Ω)_m/0.3 and, to a lesser extent, the reduced Hubble parameter h. Hence, in order to break the internal parameter degeneracies, we perform a combined likelihood analysis of the cluster sparsity estimates with cluster gas mass fraction measurements and BAO data. We find marginal constraints that are competitive with those from other standard cosmic probes: Ω_m = 0.316 ± 0.013, σ₈ = 0.757 ± 0.067 (corresponding to S₈ = 0.776 ± 0.064), and h = 0.696 ± 0.017 at 1σ. Moreover, assuming a conservative Gaussian prior on the mass bias of gas mass fraction data, we find a lower limit on the gas depletion factor Y_b,500c >= 0.89.