Cosmological Constraints on Temperature-Dependent Interaction between Dark Matter and Neutrinos
We study the influence of the temperature-dependent interaction between dark matter (DM) and neutrinos on the measurement of cosmological parameters. We pay attention to the neutrino mass effects, so that the derivation of Boltzmann equations needs to specify the concrete form of interaction. We work in a model in which the DM-neutrino scatterings are induced by a dimension-six operator, and present the details for deriving the full Boltzmann hierarchy for DM and neutrinos, including a novel method to obtain the fluid approximation for modes entering the horizon. It is shown that our interaction can induce the dark acoustic oscillation in the DM-neutrino fluid, leaving distinct signatures on the CMB and matter power spectra. By using the latest CMB and BAO datasets from Planck, DESI and ACT, the constraint on today's DM-neutrino interaction parameter for the normal neutrino mass ordering reaches $u^0_{χ-ν} \lesssim {\cal O}(10^{-13})$, nearly nine orders stronger than that for temperature-independent case in the literature. This can be understood by noting that the scattering cross section increases nearly quadratically with cosmological temperature in the early universe, leading to enhanced effects. We have investigated alternative scenarios with different neutrino mass assumptions. In particular, models with degenerate neutrino masses give rise to weaker constraint of $u^0_{χ-ν} \lesssim {\cal O}(10^{-11})$, showing the importance to incorporate the realistic neutrino mass ordering in the fits. Finally, when employing the logarithmic flat prior for $u^0_{χ-ν}$, we have shown hints to a nonzero interaction at $95\%$ CL by combining Planck, DESI and ACT data.