Mitigating baryonic effects in weak lensing with higher-order statistics

Abstract: Weak gravitational lensing is a premier cosmological probe, but its small-scale statistical power is compromised by baryonic feedback. Higher-order statistics capture non-Gaussian information that the power spectrum misses, yet their sensitivity to feedback remains a concern for Stage IV surveys. We quantify how unmodeled feedback biases the cosmological parameters inferred from the angular power spectrum (PS), starlet peak counts, and the starlet $\ell_1$-norm, and we determine the scale cuts needed to remove that bias. We also test the Bernardeau-Nishimichi-Taruya (BNT) transform as a strategy for more precise scale cuts. Our analysis is based on the cosmoGRID V1 suite, which imprints feedback on dark matter convergence maps with a baryon correction model, and on simulation-based inference with neural posterior estimation, carried out across footprints ranging from Stage III-like to the full sky. We find that biases grow with survey area, exceeding $2σ$ for all three statistics at Stage IV-like footprints, and removing them costs a substantial fraction of the signal. Restricted to these ``baryon-safe'' scales, the starlet $\ell_1$-norm still reaches a figure of merit almost twice that of the PS. The BNT transform localizes the baryonic sensitivity to the lowest transformed redshift bin and improves the PS figure of merit by a factor of $\sim$1.4, while its linear mixing of shape noise inflates the contours of the map-based higher-order statistics. Higher-order statistics therefore deliver a substantial gain over the power spectrum with no baryonic modeling at all, and an even larger one as modeling improves.