Neutrinos in N-body simulations

TL;DR

This paper assesses the limitations of N-body simulations in modeling neutrinos for cosmology, quantifying errors from neglecting relativistic effects and providing guidance on simulation accuracy for upcoming surveys.

Contribution

It offers a self-consistent theory of neutrino perturbations and quantifies the errors in matter power spectrum predictions due to relativistic neglect in N-body simulations.

Findings

Simulations overestimate neutrino free-streaming scale.

Errors in matter power spectrum are less than 0.5% for certain initial redshifts.

Relativistic effects cause up to 10% correction in neutrino suppression shape.

Abstract

In the next decade, cosmological surveys will have the statistical power to detect the absolute neutrino mass scale. N-body simulations of large-scale structure formation play a central role in interpreting data from such surveys. Yet these simulations are Newtonian in nature. We provide a quantitative study of the limitations to treating neutrinos, implemented as N-body particles, in N-body codes, focusing on the error introduced by neglecting special relativistic effects. Special relativistic effects are potentially important due to the large thermal velocities of neutrino particles in the simulation box. We derive a self-consistent theory of linear perturbations in Newtonian and non-relativistic neutrinos and use this to demonstrate that N-body simulations overestimate the neutrino free-streaming scale, and cause errors in the matter power spectrum that depend on the initial redshift of the simulations. For $z_{i} \lesssim 100$, and neutrino masses within the currently allowed range, this error is $\lesssim 0.5\%$, though represents an up to $\sim 10\%$ correction to the shape of the neutrino-induced suppression to the cold dark matter power spectrum. We argue that the simulations accurately model non-linear clustering of neutrinos so that the error is confined to linear scales.