# Interacting neutrinos in cosmology: exact description and constraints

## TL;DR

This paper provides an exact numerical analysis of neutrino self-interactions in cosmology, compares it with common approximations, and derives constraints on the interaction strength from current data, revealing a bimodal posterior distribution.

## Contribution

It implements the exact Boltzmann hierarchy for interacting neutrinos into CLASS and compares results with existing approximations, providing new constraints on neutrino self-interaction strength.

## Key findings

- Good agreement between exact approach and relaxation time approximation.
- The popular $(c_{eff}^2,c_{vis}^2)$ parameterisation fails to capture scale dependence.
- Cosmological data allow for two distinct neutrino interaction scenarios.

## Abstract

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