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

TL;DR

This paper derives the one-loop correction to the large scale matter power spectrum in cosmologies with massive neutrinos, revealing enhanced small-scale suppression beyond linear predictions, consistent with simulations.

Contribution

It provides the first systematic derivation of one-loop corrections in mixed cold+hot dark matter models including massive neutrinos, with new interaction kernels and approximations.

Findings

One-loop corrections show greater small-scale suppression than linear theory predicts.

Interaction kernels depend on neutrino energy density fraction and growth functions.

Results align with multi-component N-body simulation observations.

Abstract

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_nu and the linear growth functions of the incoming wavevectors. Compared with the f_nu=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_nu suppression predicted by linear theory, a feature also seen in multi-component N-body simulations.