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.
