Linear cosmological constraints on two-body decaying dark matter scenarios and the S8 tension

The ‘S8 tension’ is a longstanding discrepancy between the cosmic microwave background (CMB) and weak gravitational lensing determination of the amplitude of matter fluctuations, parametrized as S8 ≡ σ8(Ωm/0.3)0.5 , where σ8 is the root mean square of matter fluctuations on a 8 h −1Mpc scale, and Ωm is the total matter abundance. It was recently shown that dark matter (DM) decaying into a massless (dark radiation) and a massive (warm DM) species, with a lifetime Γ−1 ' 55 (ε/0.007)1.4 Gyrs – where ε represent the mass-energy fraction transferred to the massless component – can ease the tension. Thanks to a fast and accurate fluid approximation scheme for the warm species, we perform a comprehensive study of this 2-body decaying DM scenario, discussing in detail its dynamics and its impact on the CMB and linear matter power spectra. We then investigate the implications for the ‘S8 tension’ against a number of changes in the analysis: different S8 priors, marginalization over the lensing information in Planck data, trading Planck high−` polarization data for those from the SPTpol and ACTPol surveys, and the inclusion of the recent results from the Xenon1T collaboration. We conclude that the preference for decaying DM, apparent only when the S8 value determined from weak lensing data is added to the analysis, does not sensibly degrade the fit to any of the cosmological data-sets considered, and that the model could potentially explain the anomalous electron recoil excess reported by the Xenon1T collaboration. Furthermore, we explictly show that while current CMB data alone are not sensitive enough to distinguish between standard CDM and decaying DM, next-generation CMB observations (CMB-S4) can unambiguously detect its signature.