Constraining dark matter decay 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 di fference 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 greater than or similar to 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 di fference. 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 e ffect. From the CMB data alone, we obtain constraints of tau >= 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 >= 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.