Updated constraints on decaying cold dark matter

In this paper we update the constraints on the simple decaying cold dark matter (DCDM) model with dark radiation (DR) as decay product. We consider two different regimes of the lifetime, i.e. short-lived and long-lived, and use the most recent CMB data from Planck (2018) to infer new constraints on the decay parameters with which we compare the constraints inferred by the previous Planck data (2015). We hereby show that the newest CMB data constrains the fractional amount of DCDM twice as much as the previous data in the long-lived regime, leading to our current best 2$\sigma$ upper bound of $f_{\rm dcdm}<2.44\%$. In the short-lived regime, we get a slightly looser 2$\sigma$ upper bound of $f_{\rm dcdm}<13.1\%$ compared to the previous CMB data. If we include Baryonic Acoustic Oscillations data from BOSS DR-12, the constraints in both the long-lived and the short-lived regimes relax to $f_{\rm dcdm}<2.62\%$ and $f_{\rm dcdm}<1.49\%$, respectively. We also investigate how this model impacts the Hubble and $\sigma_8$ tensions, and we find that each of the decay regimes can slightly relieve a different one of the tensions. The model can thus not accommodate both tensions at once, and the improvements on each are not significant. We furthermore improve on previous work by thoroughly analysing the impacts of short-lived DCDM on the radiation density and deriving a mapping between short-lived DCDM and a correction, $\Delta N_{\rm eff}$, to the effective number of massless neutrino species.