  We investigate a model where neutrinos are strongly coupled to a new, light
scalar field. In this model neutrinos annihilate as soon as they become
non-relativistic in the early universe, and a non-zero neutrino mass has a
marginal effect on the matter power spectrum. However, the angular power
spectrum of the cosmic microwave background (CMB) is changed significantly
because the strongly interacting fluid of neutrinos and scalars does not
experience any anisotropic stress. Such models are strongly disfavoured by
current observations. Interestingly, this leads to the conclusion that the
relativistic energy density around the epoch of recombination must be in the
form of very weakly interacting particles. This conclusion is independent of
the specific interaction model.
