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 ∼ 5% for masses up to ∼ 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.
@article{arxiv.1510.02907,
title = {Efficient calculation of cosmological neutrino clustering with both linear and non-linear gravity},
author = {Maria Archidiacono and Steen Hannestad},
journal= {arXiv preprint arXiv:1510.02907},
year = {2016}
}