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.
