The EFT of Large Scale Structures at All Redshifts: Analytical
  Predictions for Lensing
  We study the prediction of the Effective Field Theory of Large Scale
Structures (EFTofLSS) for the matter power spectrum at different redshifts. In
previous work, we found that the two-loop prediction can match the nonlinear
power spectrum measured from $N$-body simulations at redshift zero within
approximately 2% up to $k\sim 0.6\,h\, {\rm Mpc}^{-1}$ after fixing a single
free parameter, the so-called "speed of sound". We determine the time evolution
of this parameter by matching the EFTofLSS prediction to simulation output at
different redshifts, and find that it is well-described by a fitting function
that only includes one additional parameter. After the two free parameters are
fixed, the prediction agrees with nonlinear data within approximately 2% up to
at least $k\sim 1\,h\, {\rm Mpc}^{-1}$ at $z\geq 1$, and also within
approximately 5% up to $k\sim 1.2\,h\, {\rm Mpc}^{-1}$ at $z=1$ and $k\sim
2.3\,h\, {\rm Mpc}^{-1}$ at $z=3$, a major improvement with respect to other
perturbative techniques. We also develop an accurate way to estimate where the
EFTofLSS predictions at different loop orders should fail, based on the sizes
of the next-order terms that are neglected, and find agreement with the actual
comparisons to data. Finally, we use our matter power spectrum results to
perform analytical calculations of lensing potential power spectra
corresponding to both CMB and galaxy lensing. This opens the door to future
direct applications of the EFTofLSS to observations of gravitational clustering
on cosmic scales.
