Cosmic Shear in Effective Field Theory at Two-Loop Order: Revisiting $S_8$ in Dark Energy Survey Data

Abstract

Cosmic shear is a powerful probe of cosmological distances, matter abundance and clustering in the low-redshift Universe. Cosmological parameter extraction from cosmic shear data is limited by our understanding of baryonic astrophysics, which severely restricts the range of scales used in such analyses. We show that the remaining scales are largely perturbative and can be accurately described with two-loop effective field theory (EFT) predictions. We present the first consistent analysis of the public cosmic shear data from the DES-Y3 catalogs in EFT at the two-loop order, renormalizing small-scale sensitivity in cosmic-shear predictions via a lensing-counterterm expansion and accounting for the intrinsic alignments of galaxies with spin-2 EFT predictions. We constrain the lensing amplitude competitively with standard (empirically-modeled) methods, finding $S_8 = 0.783^{+0.038}_{-0.031}$ ($S_8 = 0.802^{+0.031}_{-0.026}$ with BAO). The perturbativity of cosmic shear suggests novel opportunities for testing new physics with ongoing and upcoming cosmic shear experiments like Roman, Euclid, and LSST. As an example, we derive matter clustering constraints within the dynamical dark energy model from a combination of our DES-EFT cosmic shear likelihood, early-universe CMB priors, DESI BAO, and supernovae data, finding $S_8 = 0.824\pm 0.029$, indicating no $S_8$ tension in the growth of cosmic structure regardless of the underlying cosmological model and expansion history.

Figures (10)

• Figure 1: Contribution of different modes to the power spectrum of weak lensing convergence from bin 4 of DES-Y3. The total non-linear signal (black) is split between modes captured by one-loop ($k<k_{\rm max}^{\rm 1-loop}(\chi)$) and two-loop EFT ($k<k_{\rm max}^{\rm 2-loop}(\chi)$). Two-loop EFT captures the bulk of the lensing signal for angular scales $\ell< \ell_{\rm max}$, where $\ell_{\rm max}=319$ (for bin 4) used in this study is similar to that commonly used in weak lensing analyses based on empirical modeling, e.g. DES:2022qpf ($\ell_{\rm max}= 360$, vertical dashed line). Non-perturbative modes (green dotted) contribute $\lesssim 20\%$ of the total signal at $\ell<\ell_{\rm max}$; in our work, these are marginalized over using lensing counterterms.
• Figure 2: Cosmological constraints from applying our two-loop EFT model to DES-Y3 data in $\Lambda$CDM (w/ and w/o DESI-DR2 BAO and BBN) and $w_0 w_a$CDM (combining with DESI-DR2 BAO, late-universe marginalized Planck CMB, and SNIa from DES-Y5). Dashed solid and vertical lines mark the best-fit $\Lambda$CDM cosmology from the Planck CMB. The dashed contours show our priors on the leading lensing counterterm, which the data only loosely constrain.
• Figure S1: Left upper panel: The non-linear matter power spectrum $P(k)$ at redshifts $z = 0$--$1.2$ (color bar), computed from the $\textsc{Aemulus}-\nu$ emulator. The dashed curves show the corresponding EFT best fits up to $k_{\rm max}^{\rm 2-loop}=2k_{\rm nl}$, where the 2-loop EFT can reproduce the mock data to $0.5\%$. Right upper panel: Fractional residual of the two-loop EFT matter power spectrum relative to the $\textsc{Aemulus}-\nu$ emulator prediction, $(P^{\rm 2\text{-}loop}/P_{\rm Aemulus} - 1)$ at the same redshifts. The gray band marks the $\pm 0.5\%$ accuracy threshold. Solid curves show the residual for modes with $k < 2k_{\rm nl}(z)$ (within the nominal two-loop validity range) and dotted curves for $k > 2k_{\rm nl}(z)$ (beyond it). Lower panels: As above, but for the one-loop EFT calculations, with $k_{\rm max}^{\rm 1-loop}=0.2k_{\rm nl}$. This cut is chosen to that the EFT calculation can reproduce the data to the same $0.5\%$ accuracy.
• Figure S2: Decomposition of the weak lensing convergence power spectrum $C_\ell^{\kappa\kappa}$ for all ten tomographic bin pairs of DES-Y3, as a function of multipole $\ell$. The total signal (solid dark blue) is split into contributions from three wavenumber domains evaluated at each comoving distance $\chi$ along the line of sight via the Limber approximation $k(\ell + \tfrac{1}{2})/\chi$: modes below the one-loop validity scale $k < k_{\rm max}^{\rm 1\text{-}loop}(\chi)$ (orange dashed), modes in the two-loop regime $k_{\rm max}^{\rm 1\text{-}loop}(\chi) < k < k_{\rm max}^{\rm 2\text{-}loop}(\chi)$ (blue dot-dashed), and modes beyond the two-loop validity scale $k > k_{\rm max}^{\rm 2\text{-}loop}(\chi)$ (green dotted). The sliding scales $k_{\rm max}(\chi)$ are taken from the EFT fits to $\textsc{Aemulus}-\nu$ power spectrum emulator data in 3D. The light gray shaded region marks the conservative scale cut $\ell > \ell_{\rm max}$ applied in this analysis. Panels are labeled $(i,j)$ for source bins $i \leq j$, with higher-redshift bins toward the bottom-right. The two-loop EFT regime dominates the signal within the analysis range for all cross-correlations involving high-redshift bins.
• Figure S3: Fits to the matter power spectrum for Conservative ($< k_{\rm nl}(z)$) and Empirical ($< k^{\rm 2-loop}_{\rm max}(z)$) scale cuts varying the number of spline nodes in the counterterm time evolution model (Eq. \ref{['eqn:spline_time_dep']}). In both scenarios, the four-node spline (solid) is able to match the performance of per-redshift fits (dashed) to the power spectrum, while the three-node spline performs substantially worse. In particular, for conservative scale cuts the four-node spline predictions nowhere differ from the non-linear matter power spectrum by more than the emulator error (shown in black).