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 when the standard-model plasma temperature was $\sim \mathrm{MeV}$. 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 $G_{\text{eff}}$ and put limits on new physics in the neutrino sector from the early Universe. Within the context of conventional $\mathrm{\Lambda }\mathrm{CDM}$ parameters cosmological data are compatible with $G_{\text{eff}}\lesssim 1/(56\mathrm{MeV}{)}^2$ and neutrino free streaming might be delayed until their temperature has cooled to as low as $\sim 25\mathrm{eV}$. Intriguingly, we also find an alternative cosmology compatible with cosmological data in which neutrinos scatter off each other until $z\sim 10^4$ with a preferred interaction strength in a narrow region around $G_{\text{eff}}\simeq 1/(10\mathrm{MeV}{)}^2\simeq 8.6\times 10^8{G}_{\mathrm{F}}$, where $G_{\mathrm{F}}$ 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, our constraints on the neutrino visibility function are very general.