BASILISK IV. No $S_8$ Tension with Satellite Kinematics

We develop a novel technique to probe the $S_8$ tension, using information from the smallest scales of galaxy redshift survey data. Specifically, we use Basilisk, a Bayesian hierarchical tool for forward modeling the kinematics and abundance of satellite galaxies extracted from spectroscopic data, to first constrain the galaxy-halo connection precisely and accurately. We then demand self-consistency in that the galaxy-halo connection predicts the correct galaxy luminosity function, which constrains the halo mass function and thereby cosmology. Crucially, the method accounts for baryonic effects and is free of halo assembly bias issues. We validate the method against realistic SDSS-like mock data, demonstrating unbiased recovery of the input cosmology. Applying it to the SDSS-DR7, we infer that $\Omega_{\rm m} = 0.324 \pm 0.012$, $\sigma_8 = 0.775 \pm 0.063$ and $S_8 \equiv \sigma_8 \sqrt{\Omega_{\rm m}/0.3} = 0.81 \pm 0.05$, in perfect agreement with the cosmic microwave background constraints from Planck. The most stringent constraint is with regard to the parameter combination $\sigma_8 (\Omega_{\rm m}/0.3)^2$, which we infer to be $0.91 \pm 0.05$. Hence, unlike many low-redshift analyses of large-scale structure data, we find no indication of $S_8$ tension. We demonstrate that these results are robust to reasonable variation in the implementation of baryonification used to model the host halo's gravitational potentials in response to baryonic processes. We also highlight the importance of correctly modeling the satellite radial profile in any analysis involving small-scale information. Finally, we underscore the hidden potential of this methodology for constraining baryonic physics using data from ongoing and upcoming surveys.