Higher order corrections to the large scale matter power spectrum in the presence of massive neutrinos

We present the first systematic derivation of the one-loop correction to the large scale matter power spectrum in a mixed cold + hot dark matter cosmology with subdominant massive neutrino hot dark matter. Starting with the equations of motion for the density and velocity fields, we derive perturbative solutions to these quantities and construct recursion relations for the interaction kernels, noting and justifying all approximations along the way. We find interaction kernels similar to those for a cold dark matter only universe, but with additional dependences on the neutrino energy density fraction f ν and the linear growth functions of the incoming wavevectors. Compared with the f ν = 0 case, the one-loop corrected matter power spectrum for a mixed dark matter cosmology exhibits a decrease in small scale power exceeding the canonical ∼8 f ν suppression predicted by linear theory, a feature also seen in multi-component N -body simulations.