Interacting neutrinos in cosmology: exact description and constraints
  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
$G_{\rm eff} \simeq 3 \times 10^9 \, G_{\rm F}$.
