We discuss the viability of a light particle ($\sim 30$ eV neutrino) with strong self-interactions as a dark matter candidate. The interaction prevents the neutrinos from free-streaming during the radiation dominated regime so galaxy sized density perturbations can survive. Smaller scale perturbations are damped due to neutrino diffusion. We calculate the power spectrum in the imperfect fluid approximation, and show that it is damped at the length scale one would estimate due to neutrino diffusion. The strength of the neutrino--neutrino coupling is only weakly constrained by observations, and could be chosen by fitting the power spectrum to the observed amplitude of matter density perturbations. The main shortcoming of our model is that interacting neutrinos can not provide the dark matter in dwarf galaxies.

17 pages, Latex, accepted for publication in Phys. Rev. D