The Lensing Counter Narrative: An Effective Description of Small-Scale Clustering in Weak Lensing Power Spectra

TL;DR

Weak lensing signals blend large- and small-scale structure, making exact theoretical modeling challenging at nonlinear scales. The paper introduces lensing counterterms (LCTs), an EFT-inspired expansion that marginalizes UV contributions to C_ℓ while preserving large-scale cosmology, enabling the use of wider angular ranges without biased inferences. Using DES-Y3 data and simulated mocks, the authors show that LCTs tighten constraints on S_8 (and ω_m) by substantial factors and can absorb baryonic and exotic small-scale physics, with f_{2,0}^{UV} remaining consistent with ΛCDM. The methodology is implemented in a differentiable JAX framework (gholax) with neural-emulator accelerations, and the results suggest LCTs offer a robust, scalable path to exploiting small-scale information in future surveys such as LSST and beyond.

Abstract

We present a new formalism to separate large- and small-scale contributions to cosmic shear through $\textit{lensing counterterms}$ (LCT) inspired by effective field theory (EFT). Marginalizing over these LCTs isolates the large-scale cosmological signal in weak lensing power spectra while simultaneously constraining the impact of baryonic feedback or new physics (e.g. axion dark matter) at small scales. Our formalism removes the need for hard scale cuts in standard analyses, even when theoretical predictions are limited to below a physical cutoff $Λ$, resulting in significant improvements in constraining power -- up to $5\times$ smaller in the case of a LSST-Y10-like analysis without marginalizing over baryons when the analysis cutoff is set to $Λ= 1.0h$ Mpc$^{-1}$. We conduct a proof-of-principle analysis on the publicly available DES Y3 data, finding $S_8= 0.767\pm 0.042$ and $S_8 = 0.793\pm 0.035$ for analyses with cutoffs of $Λ= 0.5h$ Mpc$^{-1}$ and $1.0 h$ Mpc$^{-1}$, respectively, with no detection of modifications to small-scale clustering at $k > Λ$ beyond the predictions of collisionless dark matter in a $Λ$CDM universe. We make our $\texttt{JAX}$-based pipeline, $\texttt{gholax}$, integrated with intrinsic alignment predictions from the EFT of large-scale structure at 1-loop, publicly available.

Figures (16)

• Figure 1: Lensing counterterms on the DES-Y3 cosmic shear $C_{\ell}$'s. The black dashed line shows the residual contributions due to modes shorter than $k_{\rm max} = 0.5\ h$ Mpc$^{-1}$, with $5\%$ of the total signal shown in the shaded region. These contributions parametrized via lensing counterterms (Equation \ref{['eqn:lensing_ct_expansion']}), computed directly from the true nonlinear power spectrum, are shown in second, third and fourth order in blue, orange and green, showing that the expansion is perturbatively correct towards low $\ell$'s.
• Figure 2: Like Figure \ref{['fig:lensing_ct_k0p5']}, but with a cutoff of $\Lambda = 1.0\ h$ Mpc$^{-1}$.
• Figure 3: Correlation matrix computed for the DES-Y3 cosmic shear $C_\ell$'s with (bottom) and without (without) the implied theoretical covariance due to matter clustering below $k_{\rm max} = 0.5\ h$ Mpc$^{-1}$, assuming that matter at smaller scales deviates at the $20\%$ level relative to $N$-body simulations. Labels on the diagonal show the maximum fitted scale $\ell_{\rm max}$ in each block based on the convergence of the expansion as shown in Figure \ref{['fig:lensing_ct_k0p5']}.
• Figure 4: ( Top) Comparison of different parameterizations of baryonic feedback on the matter power spectrum (dashed) to a range of hydrodynamical simulation predictions as computed by the $\textrm{SP}(k)$ model Salcido23 (solid). ( Bottom) Fractional residual of the baryonic feedback parameterizations used in this work from the hydrodynamical predictions. The first two columns show fits of counterterm expansions truncated at second and fourth order, which work at the percent level to $k_{\rm max}= 0.25\, h\mathrm{Mpc}^{-1}$ and $k_{\rm max}= 0.5\, h\mathrm{Mpc}^{-1}$ respectively. The rightmost panel adds a Padé approximant to the second order expansion to control high-$k$ behavior, extending the validity of this model to $k_{\rm max}= 1\, h\mathrm{Mpc}^{-1}$ at the cost of enforcing that the leading order and next-to-leading order contributions have the opposite sign.
• Figure 5: Dependence of $S_8$ and $\omega_m$ constraints without baryon feedback on the lensing counterterm order, where $N=1$ is an analysis with no lensing counter terms. The left and right hand side figures are DES-Y3 and LSST-Y10-like analyses respectively. In the DES case, the $N=4$ expansion yields $25\%$ smaller $S_8$ uncertainties compared to the no-counterterm $N=1$ case, while the $S_8$ error is $82\%$ smaller than the $N=1$ case for LSST-Y10.