Forecasts for lifetime and fraction of Decaying Dark Matter based on redshift distortions from Euclid and BOSS

TL;DR

The paper develops a Fisher-matrix forecast to constrain decaying cold dark matter (DCDM) using redshift-space distortions from upcoming surveys, focusing on the decay fraction $\alpha_{\mathrm{dcdm}}$ and decay rate $\Gamma_{\mathrm{dcdm}}$ (lifetime $\tau_{\mathrm{dcdm}}$). The ΛDCDM model couples DCDM to dark radiation, modifying background and perturbation evolution, with fiducial parameters derived from MCMC against Planck 2018 and BAO data. By forecasting measurements of $f\sigma_8(z)$ via mock Euclid and BOSS data, the study finds weak lifetime constraints in a mixed DM scenario ($\tau_{\mathrm{dcdm}} > 1.18$ Gyr) but strong bounds when all DM is unstable ($\tau_{\mathrm{dcdm}} > 234.89$ Gyr), highlighting a strong $\alpha_{\mathrm{dcdm}}$–$\Gamma_{\mathrm{dcdm}}$ degeneracy. The results demonstrate that RSD probes are a promising, complementary avenue for testing decaying dark matter scenarios and can improve with future surveys and joint analyses.

Abstract

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.

Figures (3)

• Figure 1: 1D and 2D marginalized probability distributions for a model with both stable and unstable dark matter, using Planck-only data (red) and Planck + BAO (blue). Contours represent 68% and 95% confidence levels.
• Figure 2: Predictions of $f\sigma_8(z)$ according to different $DCDM$ models. The black line corresponding to the fiducial model from Bayesian estimate (gray curve). The points with error bars correspond to current measurements from different surveys reported in the literature.
• Figure 3: Numerical derivatives of the observable $\beta(z)=f/b$ with respect to the parameters of the DCDM model. The top panels correspond to the mixed scenario with both stable and unstable dark matter, while the bottom panel shows the fully unstable case ($\alpha_{\rm dcdm}=1$).