Résumé
Phys. Rev. D 105, 063525 (2022) 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$\sim3\sigma$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$\varepsilon\simeq 0.7 \ \%$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$0\lesssim z\lesssim1$can further test this scenario.