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 σ ₈ 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 σ ₈ (along approximately constant curves of 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, σ ₈ = 0.757 0.067 (corresponding to S ₈ = 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.

近年来，大的、完整的集群样本的可用性使得使用集群数量计数进行大量宇宙学参数推断分析成为可能。这些提供了对宇宙物质密度 Ω _m和物质密度波动幅度σ _{8 的}约束，以替代从其他标准探测器获得的值。然而，系统学的不确定性，例如质量校准偏差和选择效应，仍可能显着影响这些数据分析。因此，探索星系团宇宙学的其他代理是及时的，这些代理可以提供与从星系团数量计数获得的宇宙学约束互补的宇宙学约束。在这里，我们使用来自 LC ^{2 的}弱透镜质量估计的簇稀疏度测量值- 单个和 HSC-XXL 集群目录来推断平面 ΛCDM 模型的约束。簇稀疏性的优点是对选择和质量校准偏差不敏感。另一方面，它主要约束 Ω _m和σ ₈的退化组合（沿着近似恒定的曲线，在较小程度上，减少的哈勃参数h。因此，为了打破内部参数退化，我们执行簇稀疏估计与簇气体质量分数测量和 BAO 数据的组合似然分析。我们发现了与其他标准宇宙探测器的那些竞争的边际约束：Ω _m = 0.316 0.013, σ ₈ = 0.757 0.067（对应于S ₈ = 0.776 0.064），并且在 1 σ 时h = 0.696 0.017 。此外，假设对气体质量分数数据的质量偏差采用保守的高斯先验，我们发现气体消耗因子Y _{b ,500 c} ≳ 0.89 的下限。