Decaying dark matter models provide a physically motivated
way of channeling energy between the matter and radiation
sectors. In principle, this could affect the predicted value of the
Hubble constant in such a way as to accommodate the discrepancies
between CMB inferences and local measurements of the same. Here, we
revisit the model of warm dark matter decaying non-relativistically
to invisible radiation. In particular, we rederive the background
and perturbation equations starting from a decaying neutrino model
and describe a new, computationally efficient method of computing
the decay product perturbations up to large multipoles. We conduct
MCMC analyses to constrain all three model parameters, for the first
time including the mass of the decaying species, and assess the
ability of the model to alleviate the Hubble and σ
8
tensions, the latter being the discrepancy between the CMB and weak
gravitational lensing constraints on the amplitude of matter
fluctuations on an 8 h
-1 Mpc-1 scale. We find that the
model reduces the H
0 tension from ∼ 4σ to ∼ 3σ and neither alleviates nor worsens the S
8 ≡ σ
8
(Ω
m
/0.3)0.5 tension, ultimately showing only mild
improvements with respect to ΛCDM. However, the values of
the model-specific parameters favoured by data is found to be well
within the regime of relativistic decays where inverse processes are
important, rendering a conclusive evaluation of the decaying warm
dark matter model open to future work.