The Effective Field Theory of Large-Scale Structure in the presence of Massive Neutrinos

TL;DR

This paper develops an effective field theory framework to analytically describe matter clustering in the mildly non-linear regime with massive neutrinos, incorporating counterterms and renormalization to account for short-distance effects.

Contribution

It introduces a formalism combining Boltzmann and fluid equations, expanding in neutrino density and scale ratios, to model neutrino effects on large-scale structure.

Findings

One-loop total-matter power spectrum is approximately 16f_ν times the dark matter spectrum for large k.

Neutrinos with large free streaming wavenumber require additional counterterms similar to dark matter's speed of sound.

Counterterms can be absorbed into a shift of the effective speed of sound, simplifying the modeling of neutrino effects.

Abstract

We develop a formalism to analytically describe the clustering of matter in the mildly non-linear regime in the presence of massive neutrinos. Neutrinos, whose free streaming wavenumber ($k_{\rm fs}$) is typically longer than the non-linear scale ($k_{\rm NL}$) are described by a Boltzmann equation coupled to the effective fluid-like equations that describe dark matter. We solve the equations expanding in the neutrino density fraction $(f_\nu)$ and in $k/ k_{\rm NL}$, and add suitable counterterms to renormalize the theory. This allows us to describe the contribution of short distances to long-distance observables. Equivalently, we construct an effective Boltzmann equation where we add additional terms whose coefficients renormalize the contribution from short-distance physics. We argue that neutrinos with $k_{\rm fs}\gtrsim k_{\rm NL}$ require an additional counterterm similar to the speed of sound ($c_s$) for dark matter. We compute the one-loop total-matter power spectrum, and find that it is roughly equal to $16f_\nu$ times the dark matter one for $k$'s larger that the typical $k_{\rm fs}$. It is about half of that for smaller $k$'s. The leading contribution results from the back-reaction of the neutrinos on the dynamics of the dark matter. The counterterms contribute in a hierarchical way: the leading ones can either be computed in terms of $c_s$, or can be accounted for by shifting $c_s$ by an amount proportional to $f_\nu$.