Beware of Fake $\nu$s: The Effect of Massive Neutrinos on the Nonlinear Evolution of Cosmic Structure

TL;DR

Massive neutrinos influence cosmic structure formation primarily through their initial linear conditions, with minimal additional information gained from non-linear evolution in real space, halo, or weak lensing fields, but some in redshift space.

Contribution

This study quantifies the information about neutrino mass at the field level, showing that non-linear evolution adds little beyond the initial linear power spectrum for most observables.

Findings

Neutrino mass information is mainly in the initial linear power spectrum.

Real-space CDM and matter fields show negligible differences due to neutrinos.

Redshift space contains additional neutrino information beyond linear constraints.

Abstract

Massive neutrinos suppress the growth of cosmic structure on small, non-linear, scales. It is thus often proposed that using statistics beyond the power spectrum can tighten constraints on the neutrino mass by extracting additional information from these non-linear scales. We study the information content regarding neutrino mass at the field level, quantifying how much of this information arises from the difference in non-linear evolution between a cosmology with 1 fluid (CDM) and 2 fluids (CDM + neutrinos). We do so by running two $N$-body simulations, one with and one without massive neutrinos; both with the same phases, and matching their linear power spectrum at a given, low, redshift. This effectively isolates the information encoded in the linear initial conditions from the non-linear cosmic evolution. We demonstrate that for $k \lesssim 1\,h/{\rm Mpc}$, and for a single redshift, there is negligible difference in the real-space CDM field between the two simulations. This suggests that all the information regarding neutrino mass is in the linear power spectrum set by the initial conditions. Thus any probe based on the CDM field alone will have negligible constraining power beyond that which exists at the linear level over the same range of scales. Consequently, any probe based on the halo field will contain little information beyond the linear power. We find similar results for the matter field responsible for weak lensing. We also demonstrate that there may be much information beyond the power spectrum in the 3d matter field, however, this is not observable in modern surveys via dark matter halos or weak lensing. Finally, we show that there is additional information to be found in redshift space.