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

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.