Abstract
Despite evidence for the existence of dark matter (DM) from very high and low redshifts, a moderate amount of DM particle decay remains a valid possibility. This includes both models with very long-lived yet unstable particles or mixed scenarios where only a small fraction of dark matter is allowed to decay. In this paper, we investigate how DM particles decaying into radiation affect non-linear structure formation. We look at the power spectrum and its redshift evolution, varying both the decay lifetime (τ) and the fraction of decaying-to-total dark matter (f), and we propose a fitting function that reaches sub-percent precision below k ∼ 10 h/Mpc. Based on this fit, we perform a forecast analysis for a Euclid-like weak lensing (WL) survey, including both massive neutrino and baryonic feedback parameters. We find that with WL observations alone, it is possible to rule out decay lifetimes smaller than τ = 75 Gyr (at 95 percent CL) for the case that all DM is unstable. This constraint improves to τ = 182 Gyr if the WL data is combined with CMB priors from the Planck satellite and to τ = 275 Gyr if we further assume baryonic feedback to be fully constrained by upcoming Sunyaev-Zeldovich or X-ray data. The latter shows a factor of 3.2 improvement compared to constraints from CMB data alone. Regarding the scenario of a strongly decaying sub-component of dark matter with τ ∼ 30 Gyr or lower, it will be possible to rule out a decaying-to-total fraction of f > 0.49, f > 0.21, and f > 0.13 (at the 95 percent CL) for the same three scenarios. We conclude that the upcoming stage-IV WL surveys will allow us to significantly improve current constraints on the stability of the dark matter sector.