Cosmological Constraints from Galaxy Cluster Sparsity, Cluster Gas Mass Fraction, and Baryon Acoustic Oscillation Data

In recent years, the availability of large, complete cluster samples has enabled numerous cosmological parameter inference analyses using number counts. These have provided constraints on cosmic matter density $\Omega_m$ and amplitude fluctuations $\sigma_8$ alternative to those obtained from other standard probes. However, systematics uncertainties, such as mass calibration bias selection effects, may still significantly affect these data analyses. Hence, it is timely explore proxies galaxy cosmology that can provide complementary Here, we use measurements sparsity weak lensing estimates LC$^2$-{\it single} HSC-XXL catalogs infer a flat $\Lambda$CDM model. The advantage being insensitive bias. On hand, primarily constrains degenerate combination (along approximately constant curves $S_8=\sigma_8\sqrt{\Omega_m/0.3}$), less extent reduced Hubble $h$. in order break internal degeneracies perform combined likelihood analysis sparsities with gas fraction BAO data. We find marginal are competitive probes: $\Omega_m=0.316\pm 0.013$, $\sigma_8=0.757\pm 0.067$ (corresponding $S_8=0.776\pm 0.064$) $h=0.696\pm 0.017$ at $1\sigma$. Moreover, assuming conservative Gaussian prior data, lower limit depletion factor $Y_{b,500c}\gtrsim 0.89$.