Limits on Neutrino-Neutrino Scattering in the Early Universe

In the standard model neutrinos are assumed to have streamed across the Universe since they last scattered at the weak decoupling epoch when the temperature of the standard-model plasma was ~MeV. The shear stress of free-streaming neutrinos imprints itself gravitationally on the Cosmic Microwave Background (CMB) and makes the CMB a sensitive probe of neutrino scattering. Yet, the presence of nonstandard physics in the neutrino sector may alter this standard chronology and delay neutrino free-streaming until a much later epoch. We use observations of the CMB to constrain the strength of neutrino self-interactions G_eff and put limits on new physics in the neutrino sector from the early Universe. Recent measurements of the CMB at large multipoles made by the Planck satellite and high-l experiments are critical for probing this physics. Within the context of conventional LambdaCDM parameters cosmological data are compatible with G_eff < 1/(56 MeV)^2 and neutrino free-streaming might be delayed until their temperature has cooled to as low as ~25 eV. Intriguingly, we also find an alternative cosmology compatible with cosmological data in which neutrinos scatter off each other until z~10^4 with a preferred interaction strength in a narrow region around $G_{\rm eff} \simeq 1/({\rm 10 \, MeV})^{2} \simeq 8.6\times10^8 G_{\rm F}$, where $G_{\rm F}$ is the Fermi constant. This distinct self-interacting neutrino cosmology is characterized by somewhat lower values of both the scalar spectral index and the amplitude of primordial fluctuations. While we phrase our discussion here in terms of a specific scenario in which a late onset of neutrino free-streaming could occur, our constraints on the neutrino visibility function are very general.