Implications of the $S_8$ tension for decaying dark matter with warm decay products

Abstract

Recent weak lensing surveys have revealed that the direct measurement of the parameter combination $S_8\equiv {\sigma }_8({\Omega }_m/0.3{)}^{0.5}$ -- where ${\sigma }_8$ is a measure of the amplitude of matter fluctuations on 8 $h^{-1}$Mpc scales -- is $\sim 3\sigma$ discrepant with the value reconstructed from cosmic microwave background (CMB) data assuming the $\Lambda$CDM model. In this article, we show that it is possible to resolve the tension if dark matter (DM) decays with a lifetime of ${\Gamma }^{-1}\simeq 55\text{Gyrs}$ into one massless and one massive product, and transfers a fraction $\epsilon \simeq 0.7\%$ of its rest mass energy to the massless component. The velocity-kick received by the massive daughter leads to a suppression of gravitational clustering below its free-streaming length, thereby reducing the ${\sigma }_8$ value as compared to that inferred from the standard $\Lambda$CDM model, in a similar fashion to massive neutrino and standard warm DM. Contrarily to the latter scenarios, the time-dependence of the power suppression and the free-streaming scale allows the 2-body decaying DM scenario to accommodate CMB, baryon acoustic oscillation, growth factor and un-calibrated supernova Ia data. We briefly discuss implications for DM model building, galactic small-scale structure problems and the recent Xenon-1T excess. Future experiments measuring the growth factor to high accuracy at $0\lesssim z\lesssim 1$ can further test this scenario.

Comments: 5+9 pages, 8 figures. Added calculation of Q_DMAP tension metric and bayesian evidence. Added LDDM+Mnu run. Included discussion on linear priors and lower bound on epsilon parameter. v2 matches the published PRD version. Comments welcome!