Title:A fresh look at linear cosmological constraints on a decaying dark matter component

Abstract:We consider a cosmological model in which a fraction $f$ of the Dark Matter (DM) is allowed to decay in an invisible relativistic component, and compute the resulting constraints on both the decay width (or inverse lifetime) $\Gamma$ and $f$ from purely gravitational arguments. We report a full derivation of the Boltzmann hierarchy, correcting a mistake in previous literature, and compute the impact of the decay --as a function of the lifetime-- on the CMB and matter power spectra. From CMB only, we obtain that no more than 3.8 % of the DM could have decayed in the time between recombination and today (all bounds quoted at 95 % CL). We also comment on the important application of this bound to the case where primordial black holes constitute DM, a scenario notoriously difficult to constrain. For lifetimes longer than the age of the Universe, the bounds can be cast as $f\Gamma < 6.3\times10^{-3}$ Gyr$^{-1}$. For the first time, we also checked that degeneracies with massive neutrinos are broken when information from the large scale structure is used. Even secondary effects like CMB lensing suffice to this purpose. Decaying DM models have been invoked to solve a possible tension between low redshift astronomical measurements of $\sigma_8$ and $\Omega_{\rm m}$ and the ones inferred by Planck. We reassess this claim finding that with the most recent BAO, HST and $\sigma_8$ data extracted from the CFHT survey, the tension is only slightly reduced despite the two additional free parameters, loosening the bound to $f\Gamma < 15.9\times10^{-3}$ Gyr$^{-1}$. The bound however improves to $f\Gamma < 5.9\times10^{-3}$ Gyr$^{-1}$ if only data consistent with the CMB are included. This highlights the importance of establishing whether the tension is due to real physical effects or unaccounted systematics, for settling the reach of achievable constraints on decaying DM.