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 (EFT) of large-scale structure for cosmic density and momentum fields. We show that the finite part of the two-loop calculation and its counterterms introduces an apparent scale dependence for the leading-order parameter c_s² of the EFT starting at k =0.1 h Mpc^-1 . 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^-1 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_s² seen in simulations. It is also able to capture the scale dependence of the density power spectrum up to k ≈0.3 h Mpc^-1 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^-1 . 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.