Interacting neutrinos in cosmology: exact description and constraints

Abstract

We consider the impact of neutrino self-interactions described by an\neffective four-fermion coupling on cosmological observations. Implementing the\nexact Boltzmann hierarchy for interacting neutrinos first derived in\n[arxiv:1409.1577] into the Boltzmann solver CLASS, we perform a detailed\nnumerical analysis of the effects of the interaction on the cosmic microwave\nbackground (CMB) anisotropies, and compare our results with known\napproximations in the literature. While we find good agreement between our\nexact approach and the relaxation time approximation used in some recent\nstudies, the popular $\\left( c_{\\text{eff}}^2,c_{\\text{vis}}^2\n\\right)$-parameterisation fails to reproduce the correct scale dependence of\nthe CMB temperature power spectrum. We then proceed to derive constraints on\nthe effective coupling constant $G_{\\text{eff}}$ using currently available\ncosmological data via an MCMC analysis. Interestingly, our results reveal a\nbimodal posterior distribution, where one mode represents the standard\n$\\Lambda$CDM limit with $G_{\\rm eff} \\lesssim 10^8 \\, G_{\\rm F}$, and the other\na scenario in which neutrinos self-interact with an effective coupling constant\n$G_{\\rm eff} \\simeq 3 \\times 10^9 \\, G_{\\rm F}$.\n