Decaying Dark Matter and Lyman-$\alpha$ forest constraints

Decaying Cold Dark Matter (DCDM) is a model that is currently under investigation regarding primarily the $S_8$ tension between cosmic microwave background (CMB) and certain large-scale structure measurements. The decay into one massive and one (or more) massless daughter particle(s) leads to a suppression of the power spectrum in the late universe that depends on the relative mass splitting $\epsilon=(1-m^2/M^2)/2$ between the mother and massive daughter particle as well as the lifetime $\tau$. In this work we investigate the impact of the BOSS DR14 one-dimensional Lyman-$\alpha$ forest flux power spectrum on the DCDM model using a conservative effective model approach to account for astrophysical uncertainties. Since the suppression of the power spectrum due to decay builds up at low redshift, we find that regions in parameter space that address the $S_8$ tension can be well compatible with the Lyman-$\alpha$ forest. Nevertheless, for values of the degeneracy parameter $\epsilon\sim 0.1-0.5\%$, for which the power suppression occurs within the scales probed by BOSS Lyman-$\alpha$ data, we find improved constraints compared to previous CMB and galaxy clustering analyses, obtaining $\tau\gtrsim 18$ Gyrs for small mass splitting. Furthermore, our analysis of the BOSS Lyman-$\alpha$ flux power spectrum allows for values $\tau\sim 10^2$ Gyrs, $\epsilon\sim 1\%$, that have been found to be preferred by a combination of Planck and galaxy clustering data with a KiDS prior on $S_8$, and we even find a marginal preference within this regime.