Towards the Two-Loop EFTofLSS in Galaxy Lensing Surveys

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.