The Effective Field Theory of Large Scale Structure at Two Loops: the apparent scale dependence of the speed of sound

TL;DR

This paper analyzes the two-loop Effective Field Theory of Large Scale Structure, revealing an apparent scale dependence in the sound speed parameter and proposing a one-parameter model to accurately describe power spectra up to higher wavenumbers.

Contribution

It introduces a one-parameter ansatz to account for the scale dependence of EFT parameters at two loops, improving the modeling of large scale structure power spectra.

Findings

The two-loop calculation induces an apparent scale dependence in the sound speed parameter.

A one-parameter model effectively captures the scale dependence of the density power spectrum up to k≈0.3 h/Mpc.

Two-loop results reduce the need for IR resummation at k<0.2 h/Mpc.

Abstract

We study the Effective Field Theory of Large Scale Structure for cosmic density and momentum fields. We show that the finite part of the two-loop calculation and its counterterms introduce an apparent scale dependence for the leading order parameter $c_\text{s}^2$ of the EFT starting at k=0.1 h/Mpc. These terms limit the range over which one can trust the one-loop EFT calculation at the 1 % level to k<0.1 h/Mpc at redshift z=0. We construct a well motivated one parameter ansatz to fix the relative size of the one- and two-loop counterterms using their high-k sensitivity. Although this one parameter model is a very restrictive choice for the counterterms, it explains the apparent scale dependence of $c_\text{s}^2$ seen in simulations. It is also able to capture the scale dependence of the density power spectrum up to k$\approx$ 0.3 h/Mpc at the 1 % level at redshift $z=0$. Considering a simple scheme for the resummation of large scale motions, we find that the two loop calculation reduces the need for this IR-resummation at k<0.2 h/Mpc. Finally, we extend our calculation to momentum statistics and show that the same one parameter model can also describe density-momentum and momentum-momentum statistics.