Forecasts for lifetime and fraction of Decaying Dark Matter based on redshift distortions from Euclid and BOSS
In this work we forecast constraints on models of decaying dark matter (DCDM) by using redshift-space-distortion (RSD) measurements implemented in a Fisher information matrix. In particular, we focus on the fraction of unstable dark matter, $α_{\mathrm{dcdm}}$ respect to the ordinary CDM component, and the decay rate, $Γ_{\mathrm{dcdm}}$ as the key parameters of the model. Fiducial values are derived from a MontePython MCMC analysis. The derivatives of the growth-related observable, $fσ_8(z)$ with respect to the parameters are numerically around the fiducial model. For the Fisher analysis, we employ mock data designed for upcoming surveys, particularly Euclid and BOSS, where RSD measurements yield constraints on $fσ_8.$ Our results show that when both stable and unstable components are allowed, constrains on the DCDM lifetime remain weak, with $τ_{\mathrm{dcdm}}>1.18$ Gyr. In the limiting case of fully unstable dark matter ($α_{\mathrm{dcdm}}=1$), the uncertainty improves to $τ_{\mathrm{dcdm}}>235.89$ Gyr. Our findings highlight the potential of RSD probes in testing and complementing decaying dark matter scenarios.