Loop corrections to the power spectrum for massive neutrino cosmologies with full time- and scale-dependence

TL;DR

This paper develops an algorithm to accurately compute loop corrections to the matter power spectrum in cosmologies with massive neutrinos, accounting for full time and scale dependence, and compares it to simplified models.

Contribution

It introduces a hybrid Boltzmann/two-fluid model and an algorithm for precise 1- and 2-loop power spectrum calculations with massive neutrinos, improving upon approximate methods.

Findings

Deviations above 1% for k > 0.15 h/Mpc at z=0 using simplified schemes.

Sub-percent agreement on weakly non-linear scales at z=0.5.

Impact of EdS approximation on 2-loop power spectrum for massless neutrinos.

Abstract

Loop corrections to the power spectrum are frequently computed using approximate non-linear kernels adopted from an Einstein de-Sitter (EdS) cosmology. We present an algorithm that allows us to take the full time- and scale-dependence of the underlying fluid dynamics into account, and apply it to assess the impact of neutrino free-streaming on the 1- and 2-loop matter power spectrum. Neutrino perturbations are described by a hybrid Boltzmann/two-fluid model, that we show to agree with the CLASS Boltzmann solution at the linear level when using an appropriate effective neutrino sound velocity. We then use this scheme at 1- and 2-loop to perform a precision comparison of the matter power spectrum with simplified treatments of massive neutrinos. For a commonly adopted scheme using cold dark matter+baryon perturbations and EdS kernels to compute non-linear corrections, we find deviations above 1% for k > 0.15 h/Mpc at z=0, and sub-percent agreement on weakly non-linear scales at z=0.5. We also demonstrate the impact of the EdS approximation on the 2-loop power spectrum for massless neutrinos.