Testing decaying dark matter models as a solution to the $S_8$ tension with the thermal Sunyaev-Zel'dovich effect

Considering possible solutions to the $S_8$ tension between the Planck cosmic microwave background (CMB) measurement and low-redshift probes, we extended the standard $\Lambda$CDM cosmological model by including decay of dark matter (DDM). We first tested the DDM model in which dark matter decays into a form of noninteracting dark radiation. Under this DDM model, we investigated the impacts of DDM on the Sunyaev Zel'dovich (SZ) effect by varying the decay lifetime, $\Gamma^{-1}$, including the background evolution in cosmology and the nonlinear prescription in the halo mass function. We performed a cosmological analysis under the assumption of this extended cosmological model by combining the latest high-redshift Planck CMB measurement and low-redshift measurements of the SZ power spectrum as well as the baryonic acoustic oscillations (BAO) and luminosity distances to type Ia supernovae (SNIa). Our result shows a preference for $\Gamma^{-1} \sim 220$ Gyr with a lower bound on the decay lifetime of $\sim$ 38 Gyr at 95\% confidence level. Additionally, we tested the other DDM model in which dark matter decays into warm dark matter and dark radiation. This model supports $\Gamma^{-1} \sim 137$ Gyr to resolve the $S_8$ tension with a lower bound on the decay lifetime of $\sim$ 24 Gyr at 95\% confidence level. Comparing these two models, we find that the second leads to slightly better reconciliation of the $S_8$ tension.