What Galaxy Clusters Have to Say About Dynamical Dark Energy and $H_0$

Abstract

We show that, in flat $\Lambda$CDM, low-redshift structure probes -- cluster abundances, 3$\times$2-point analyses, and full-shape clustering -- are mutually consistent, jointly delivering precise constraints on $\sigma_8$ and $\Omega_{\rm m}$ that agree with geometrical datasets (CMB+BAO+SN). In $w_0w_a$CDM, adding clusters to the geometry dataset reduces the evidence for evolving dark energy while relaxing the $H_0$ tension, suggesting a $\Lambda$CDM evolution of the late-time Universe and a sound horizon that differs from its standard value.