Munshi, D; Jung, G; Kitching, TD; McEwen, J; Liguori, M; Namikawa, T; Heavens, A; (2023) Position-dependent correlation function of weak-lensing convergence. Physical Review D , 107 (4) , Article 043516. 10.1103/PhysRevD.107.043516.

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Abstract

We provide a systematic study of the position-dependent correlation function in weak-lensing convergence maps and its relation to the squeezed limit of the three-point correlation function (3PCF) using state-of-the-art numerical simulations. We relate the position-dependent correlation function to its harmonic counterpart, i.e., the position-dependent power spectrum or equivalently the integrated bispectrum (IB). We use a recently proposed improved fitting function, BiHalofit, for the bispectrum to compute the theoretical predictions as a function of source redshifts. In addition to low redshift results (zs=1.0-2.0) we also provide results for maps inferred from lensing of the cosmic microwave background (CMB), i.e., zs=1100. We include a Euclid-type realistic survey mask and noise. In agreement with the recent studies on the position-dependent power spectrum, we find that the results from simulations are consistent with the theoretical expectations when appropriate corrections are included. Performing a rough estimate, we find that the signal-to-noise (S/N) for the detection of position-dependent correlation function from Euclid-type mask with fsky=0.35, can range between 6-12 depending on the value of the intrinsic ellipticity distribution parameter σϵ=0.3-1.0. For reconstructed κ maps using an ideal CMB survey the S/N≈1.8. We also found that a 10% deviation in σ8 can be detected using IB for the optimistic case of σϵ=0.3 with a S/N≈5. The S/N for such detection in case of ωM is lower.

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