We investigate signatures of neutrino scattering in the Cosmic Microwave Background (CMB) and matter power spectra, and the extent to which present cosmological data can distinguish between a free streaming or tightly coupled fluid of neutrinos. If neutrinos have strong non-standard interactions, for example, through the coupling of neutrinos to a light boson, they may be kept in equilibrium until late times. We show how the power spectra for these models differ from more conventional neutrino scenarios, and use CMB and large scale structure data to constrain these models. CMB polarization data improves the constraints on the number of massless neutrinos, while the Lyman--$α$ power spectrum improves the limits on the neutrino mass. Neutrino mass limits depend strongly on whether some or all of the neutrino species interact and annihilate. The present data can accommodate a number of tightly-coupled relativistic degrees of freedom, and none of the interacting-neutrino scenarios considered are ruled out by current data -- although considerations regarding the age of the Universe disfavor a model with three annihilating neutrinos with very large neutrino masses.

17 pages, 14 figures, minor changes and references added, published in Phys. Rev. D