The EFT of Large Scale Structures at All Redshifts: Analytical Predictions for Lensing

TL;DR

This paper advances the Effective Field Theory of Large Scale Structures by providing accurate analytical predictions for the matter power spectrum across redshifts, improving agreement with simulations and enabling applications to gravitational lensing observations.

Contribution

It extends the EFTofLSS to all redshifts with a two-parameter model, achieving high-precision predictions for the matter power spectrum and lensing potentials.

Findings

Two-loop EFTofLSS matches nonlinear power spectrum within 2% up to high k.

The time evolution of the sound speed parameter is well-described by a simple fitting function.

The method accurately predicts the scale where EFTofLSS predictions break down.

Abstract

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.