It is not σ_8: constraining the non-linear matter power spectrum with the Dark Energy Survey Year-5 supernova sample

The weak gravitational lensing magnification of Type Ia supernovae (SNe Ia) is sensitive to the matter power spectrum on scales k > 1h Mpc⁻¹, making it unwise to interpret SNe Ia lensing in terms of power on linear scales. We compute the probability density function of SNe Ia magnification as a function of standard cosmological parameters, plus an empirical parameter A_mod which describes the suppression or enhancement of matter power on non-linear scales compared to a cold dark matter only model. While baryons are expected to enhance power on the scales relevant to SN Ia lensing, other physics such as neutrino masses or non-standard dark matter may suppress power. Using the Dark Energy Survey Year-5 sample, we find A_mod = 0.77⁺₋₀^0.₄₀⁶⁹ (68 per cent credible interval around the median). Although the median is consistent with unity there are hints of power suppression, with A_mod < 1.09 at 68 per cent credibility.