A frequentist view on the two-body decaying dark matter model

Abstract

Decaying dark matter (DDM) has emerged as an interesting framework to extend the $\Lambda$-cold-dark-matter (LCDM) model, as many particle physics models predict that dark matter may not be stable over cosmic time and can impact structure formation. In particular, a model in which DDM decays at a rate $\Gamma$ and imprints a velocity kick $v$ onto its decay products leads to a low amplitude of fluctuations, as quantified by the parameter $S_8$, in better agreement with that measured by some weak lensing surveys. Bayesian analyses have provided mixed conclusions regarding its viability, with a reconstructed clustering amplitude only slightly below the standard LCDM value. In this paper, we contrast previous results with a frequentist analysis of Planck and SDSS BAO data. We find that the $68\%$ confidence level region corresponds to a decay half-life of $6.93^{+7.88}_{-2.85}$Gyr and a velocity kick of $1250^{+1450}_{-1000}$~km/s. These $1\sigma$ constraints strongly differ from their Bayesian counterparts, indicating the presence of volume effect in the Bayesian analysis. Moreover, we find that under the DDM model, the frequentist analysis predicts lower values of $S_8$, in agreement with those found by KiDS-1000 and DES-Y3 at $\sim 1.5\sigma$. We further show that previously derived KiDS-1000 constraints that appeared to exclude the best-fit model from Planck data were driven by priors on the primordial amplitude $A_s$ and spectral index $n_s$. When those are removed from the analysis, KiDS-1000 constraints on the DDM parameters are fully relaxed. It is only when applying Planck-informed priors on $A_s$ and $n_s$ to the KiDS-1000 analysis that one can constrain the model. We note that without such priors, the scales best measured by KiDS-1000 do not exactly match the $S_8$ kernel, so $S_8$ constraints should not be applied directly to a model in place of the full likelihood.