Towards the Two-Loop EFTofLSS in Galaxy Lensing 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 $S_8=σ_8\sqrt{Ω_{\rm m}/0.3}$ 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.

Figures (11)

• Figure 1: The $67\%$ and $95\%$ bands for $\chi^2_{\rm MPS}$ as a function of $k_{\vec{c}}$, the largest $k$ used to fit the counterterms at $z=0$, rescaled by the linear growth factor, computed from $899$ cosmologies and across $512$ redshifts. The one-loop is displayed in the upper panel and two-loop in the lower panel. The gray band shows the $\chi^2_{\rm MPS}$, defined in Eq. (\ref{['eq:chi2MPS']}), if we allow the coefficients to take any value that minimizes the $\chi^2_{\rm MPS}$, while the blue bands show the result taking $k_{\vec{c}} = 0.15/D(z)\,h/$Mpc for the one-loop and $k_{\vec{c}} = 0.7/D(z)\,h/$Mpc for the two-loop (vertical dashed lines), and use it at another (lower) $k_{\vec{c}}$. Using the chosen $k_{\vec{c}}$, even if those are beyond the perturbative regime, gives a good fit to the power spectrum, as seen by the relatively stable $\chi^2_{\rm MPS}$.
• Figure 2: The best fit values of the counterterms fit to the EE2 power spectrum as a function of redshift. The bottom panels display the values for $\vec{c}$ at two loops, while the top panel shows the single effective sound speed at one-loop. The solid line is the median across the $899$ cosmologies we used to train the emulators, and the shaded regions show the 67% confidence interval across the $899$ cosmologies. These were fit at the values of $k_{\vec{c}}$, as described in Fig. \ref{['fig:coeffs_ee2ref']}.
• Figure 3: The redshift distribution of source galaxies used in our Roman cosmic shear forecast. The $n(z)$ in each of the $8$ redshift bins are normalized so that they integrate to unity.
• Figure 4: The UV (dashed colored) and IR (dotted colored) contributions to the total (solid black) cosmic shear for redshift bins with $i=j$, as explained in Sec. \ref{['sec:scalecuts']}. The upper eight panels display $\xi_+$ and the lower eight displays $\xi_-$. As $k_{\rm UV}$ increases, $\xi_{\pm, {\rm UV}}$ moves to smaller scales (smaller $\theta$).
• Figure 5: The adopted scalecuts for the shear-shear correlations, as outlined in Sec. \ref{['sec:scalecuts']}. We only display the cuts for the same galaxy sample redshift bins $(i=j)$. The top panel corresponds to the UV-IR split with $\alpha=0.01$, while we use $\alpha=0.05$ for the bottom panel. The conservative $\alpha_{0.01}$ scale cuts do not have any unmasked data until $k_{\rm UV}=0.25$$h$/Mpc, while the more aggressive choice allows one to start at $k_{\rm UV}=0.15$$h$/Mpc. Additionally, $\alpha_{0.01}$ always masks more data than the $\alpha_{0.05}$, and both are monotonic in $k_{\rm UV}$.