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.
