Towards the Two-Loop EFTofLSS in Galaxy Lensing Surveys

TL;DR

This paper develops a two-loop effective field theory framework for galaxy lensing surveys, enabling accurate modeling of the matter power spectrum across scales and redshifts, and forecasts its potential for precise cosmological constraints.

Contribution

It introduces a two-loop EFTofLSS approach with neural network emulators, redshift calibration, and PCA-based parameter reduction for robust small-scale cosmological analysis.

Findings

Achieves unbiased $S_8$ constraints with about 1% relative error.

Extends the scale reach beyond one-loop EFT and dark matter-only models.

Provides a robust method for small-scale information extraction from future surveys.

Abstract

Extracting cosmological information from Stage IV weak lensing surveys requires non-linear modelling of the matter power spectrum that is accurate across a broad range of scales and redshifts and robust to baryonic feedback. We forecast the application of the two-loop effective field theory of large-scale structure (EFTofLSS) to Roman Space Telescope, carefully considering parameterization, scale cuts, and priors. We develop neural network emulators for the two-loop integrals, allowing rapid evaluation of the likelihood. Weak lensing demands a continuous-in-redshift description of the EFT, potentially introducing tens of nuisance parameters. We address this by calibrating the counterterm redshift evolution against the Euclid Emulator 2 and accounting for the residual freedom in redshift with spline functions. A principal component analysis of the free parameters reduces the dimensionality to a few degrees of freedom that the data can constrain. Next, we calibrate the priors on those degrees of freedom by using a suite of hydrodynamical simulations. We forecast the $S_8$ constraints as a function of scale cuts, showing that the two-loop EFT with Roman cosmic shear provides unbiased $S_8=\sigma_8\sqrt{\Omega_{\rm m}/0.3}$ constraints with relative errors of about $0.9\%$ and $1.4\%$ when allowing for $5\%$ and $1\%$ contamination from ultraviolet modes, respectively. The two-loop EFT improves the scale reach beyond the one-loop EFT and non-linear dark matter-only models when baryonic effects are included. This framework provides a robust path for extracting small-scale information from future cosmic shear data.