Cosmology from the integrated shear 3-point correlation function: simulated likelihood analyses with machine-learning emulators

Abstract

The integrated shear 3-point correlation function ${\zeta }_{\pm }$ measures the correlation between the local shear 2-point function ${\xi }_{\pm }$ and the 1-point shear aperture mass in patches of the sky. Unlike other higher-order statistics, ${\zeta }_{\pm }$ can be efficiently measured from cosmic shear data, and it admits accurate theory predictions on a wide range of scales as a function of cosmological and baryonic feedback parameters. Here, we develop and test a likelihood analysis pipeline for cosmological constraints using ${\zeta }_{\pm }$. We incorporate treatment of systematic effects from photometric redshift uncertainties, shear calibration bias and galaxy intrinsic alignments. We also develop an accurate neural-network emulator for fast theory predictions in MCMC parameter inference analyses. We test our pipeline using realistic cosmic shear maps based on $N$-body simulations with a DES Y3-like footprint, mask and source tomographic bins, finding unbiased parameter constraints. Relative to ${\xi }_{\pm }$-only, adding ${\zeta }_{\pm }$ can lead to $\approx 10-25\%$ improvements on the constraints of parameters like $A_s$ (or ${\sigma }_8$) and $w_0$. We find no evidence in ${\xi }_{\pm }+{\zeta }_{\pm }$ constraints of a significant mitigation of the impact of systematics. We also investigate the impact of the size of the apertures where ${\zeta }_{\pm }$ is measured, and of the strategy to estimate the covariance matrix ($N$-body vs. lognormal). Our analysis solidifies the strong potential of the ${\zeta }_{\pm }$ statistic and puts forward a pipeline that can be readily used to improve cosmological constraints using real cosmic shear data.

21 pages, 11 figures, 3 tables. Comments welcome

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• Clustering of the extreme: A theoretical description of weak lensing critical points power spectra in the mildly nonlinear regime
• Interpretability of deep-learning methods applied to large-scale structure surveys
• $\text{SBi3PCF:}$ Simulation-based inference with the integrated 3PCF
• Non-linear infusion of intrinsic alignment and source clustering: impact on non-Gaussian cosmic shear statistics