Voids fill us in on rising cosmology tensions

We investigate the main tensions within the current standard model of cosmology from the perspective of the main statistics of cosmic voids, using the final BOSS DR12 data set. For this purpose, we present the first estimate of the $S_8\equiv \sigma_8\sqrt{\Omega_{\rm m}/0.3}$ and $H_0$ parameters obtained from void number counts and shape distortions. To analyze void counts we rely on an extension of the popular volume-conserving model for the void size function, tailored to the application on data, including geometric and dynamic distortions. We calibrate the two nuisance parameters of this model with the official BOSS collaboration mock catalogs and propagate their uncertainty through the statistical analysis of the BOSS void number counts. The constraints from void shapes come from the study of the geometric distortions of the stacked void-galaxy cross-correlation function. In this $Letter$ we focus our analysis on the $\Omega_{\rm m} - \sigma_8$ and $\Omega_{\rm m} - H_0$ parameter planes and derive the marginalized constraints $S_8 = 0.813^{+0.093}_{-0.068}$ and $H_0 = 67.3^{+10.0}_{-9.1} \ \mathrm{km} \ \mathrm{s}^{-1} \ \mathrm{Mpc}^{-1}$, which are fully compatible with constraints from the literature. These results are expected to notably improve in precision when analyzed jointly with independent probes and will open a new viewing angle on the rising cosmological tensions in the near future.