Baryonic effects in the Effective Field Theory of Large-Scale Structure
  and an analytic recipe for lensing in CMB-S4
  Upcoming Large-Scale Structure surveys will likely become the next leading
sources of cosmological information, making it crucial to have a precise
understanding of the influence of baryons on cosmological observables. The
Effective Field Theory of Large-Scale Structure (EFTofLSS) provides a
consistent way to predict the clustering of dark matter and baryons on large
scales, where their leading corrections in perturbation theory are given by a
simple and calculable functional form even after the onset of baryonic
processes. In this paper, we extend the two-fluid-like system up to two-loop
order in perturbation theory. Along the way, we show that a new linear
counterterm proportional to the relative velocity of the fluids could
generically be present, but we show that its effects are expected to be small
in our universe. Regardless, we show how to consistently perform perturbation
theory in the presence of this new term. We find that the EFTofLSS at two-loop
order can accurately account for the details of baryonic processes on large
scales. We compare our results to a hydrodynamical $N$-body simulation at many
redshifts and find that the counterterms associated with the leading
corrections to dark matter and baryons start to differ between redshifts $z
\approx 3$ and $z \approx 2$, signaling the onset of star-formation physics. We
then use these fits to compute the lensing power spectrum, show that the
understanding of baryonic processes will be important for analyzing CMB-S4
data, and show that the two-loop EFTofLSS accurately captures these effects for
$\ell \lesssim 2000$. Our results are also potentially of interest for current
and future weak lensing surveys.
