Efficient calculation of cosmological neutrino clustering with both linear and non-linear gravity

TL;DR

This paper presents a new efficient method for calculating neutrino clustering in cosmology, achieving high precision in both linear and non-linear regimes by combining simplified Boltzmann hierarchy approximations with semi-analytic non-linear gravitational potentials.

Contribution

It introduces a novel approximation for the Boltzmann hierarchy and demonstrates accurate neutrino power spectrum calculations in non-linear regimes using semi-analytic methods.

Findings

Neutrino power spectrum can be computed with better than 5% accuracy for masses up to 1 eV.

Matter and CMB power spectra are calculated more precisely than previous methods.

Results agree closely with N-body simulation data.

Abstract

We study in detail how neutrino perturbations can be followed in linear theory by using only terms up to $l=2$ in the Boltzmann hierarchy. We provide a new approximation to the third moment and demonstrate that the neutrino power spectrum can be calculated to a precision of better than $\sim$ 5% for masses up to $\sim$ 1 eV. The matter and CMB power spectra can be calculated far more precisely and typically at least a factor of a few better than with existing approximations. We then proceed to study how the neutrino power spectrum can be reliably calculated even in the presence of non-linear gravitational clustering by using the full non-linear gravitational potential derived from semi-analytic methods based on $N$-body simulations in the Boltzmann evolution hierarchy. Our results agree extremely well with results derived from $N$-body simulations.