Abstract
The recent tension in the value of the cosmological parameter $S_8 \equiv
\sigma_8(\Omega_M/0.3)^{1/2}$, which represents the amplitude of the matter
density fluctuations of the universe, has not been resolved. In this work, we
present constraints on $S_8$ with the X-ray angular power spectra of clusters
and groups measured with the half-sky map from the eROSITA All Sky Survey data
release 1 (eRASS1). Thanks to the extensive sky coverage of eRASS1, its power
spectrum achieves unprecedented precision compared to previous measurements.
Using a well-calibrated, physical halo gas model that includes astrophysics of
feedback and non-thermal pressure support, we obtain $S_8 =
0.80^{+0.02}_{-0.01}$ with 1$\sigma$ uncertainty that is competitive against
other cosmological probes. Our derived $S_8$ value is smaller than the primary
CMB measurements from Planck, but still consistent to within $1\sigma$. We also
obtain constraints on the astrophysics of feedback, non-thermal pressure,
equation of state in cluster cores, and gas boundaries in clusters and groups.
We discuss how additional X-ray observations, and cosmological surveys in
microwave and optical, will further improve the cosmological constraints with
the angular power spectrum. Our work demonstrates that the angular power
spectrum of clusters and groups is a promising probe of both cosmology and
astrophysics.