Constraining dark matter decays with cosmic microwave background and weak lensing shear observations

From observations at low and high redshifts, it is well known that the bulk of dark matter (DM) has to be stable or at least very long-lived. However, the possibility that a small fraction of DM is unstable or that all DM decays with a half-life time ($\tau$) significantly longer than the age of the Universe is not ruled out. One-body decaying dark matter (DDM) consists of a minimal extension to the $\Lambda$CDM model. It causes a modification of the cosmic growth history as well as a suppression of the small-scale clustering signal, providing interesting consequences regarding the $S_8$ tension, which is the observed difference in the clustering amplitude between weak-lensing (WL) and cosmic microwave background (CMB) observations. In this paper, we investigate models in which a fraction or all DM decays into radiation, focusing on the long-lived regime, that is, $\tau \gtrsim H_0^{-1}$ ( $H_0^{-1}$ being the Hubble time). We used WL data from the Kilo-Degree Survey (KiDS) and CMB data from Planck. First, we confirm that this DDM model cannot alleviate the $S_8$ difference. We then show that the most constraining power for DM decay does not come from the nonlinear WL data, but from CMB via the integrated Sachs-Wolfe effect. From the CMB data alone, we obtain constraints of $\tau \geq 288$~Gyr if all DM is assumed to be unstable, and we show that a maximum fraction of $f=0.07$ is allowed to decay assuming the half-life time to be comparable to (or shorter than) one Hubble time. The constraints from the KiDS-1000 WL data are significantly weaker, $\tau \geq 60$~Gyr and $f<0.34$. Combining the CMB and WL data does not yield tighter constraints than the CMB alone, except for short half-life times, for which the maximum allowed fraction becomes $f=0.03$. All limits are provided at the 95% confidence level.