Tree-Level Bispectrum in the Effective Field Theory of Large-Scale Structure extended to Massive Neutrinos

TL;DR

This paper calculates the tree-level bispectrum of dark matter considering massive neutrinos within the effective field theory framework, revealing significant neutrino effects on small scales and minimal impact on large scales.

Contribution

It extends the EFTofLSS to include massive neutrinos and provides a perturbative method to compute their impact on the bispectrum in the mildly non-linear regime.

Findings

Neutrinos increase the bispectrum by about 16f_ν on small scales.

Largest neutrino effect is from back-reaction on dark matter growth.

Neutrino contribution is much smaller on large scales.

Abstract

We compute the tree-level bispectrum of dark matter in the presence of massive neutrinos in the mildly non-linear regime in the context of the effective field theory of large-scale structure (EFTofLSS). For neutrinos, whose typical free streaming wavenumber ($k_{\rm fs}$) is longer than the non-linear scale ($k_{\mathrm{NL}}$), we solve a Boltzmann equation coupled to the effective fluid equation for dark matter. We solve perturbatively the coupled system by expanding in powers of the neutrino density fraction ($f_{\nu}$) and the ratio of the wavenumber of interest over the non-linear scale ($k/k_{\mathrm{NL}}$) and add suitable counterterms to remove the dependence from short distance physics. For equilateral configurations, we find that the total-matter tree-level bispectrum is approximately $16f_{\nu}$ times the dark matter one on short scales ($k > k_{\rm fs}$). The largest contribution stems from the back-reaction of massive neutrinos on the dark matter growth factor. On large scales ($k < k_{\rm fs}$) the contribution of neutrinos to the bispectrum is smaller by up to two orders of magnitude.