The integrated 3-point correlation function of cosmic shear

Abstract

We present the integrated 3-point shear correlation function iζ ± -a higher-order statistic of the cosmic shear field -which can be directly estimated in wide-area weak lensing surveys without measuring the full 3-point shear correlation function, making this a practical and complementary tool to 2-point statistics for weak lensing cosmology. We define it as the 1-point aperture mass statistic M ap measured at different locations on the shear field correlated with the corresponding local 2-point shear correlation function ξ ± . Building upon existing work on the integrated bispectrum of the weak lensing convergence field, we present a theoretical framework for computing the integrated 3-point function in real space for any projected field within the flat-sky approximation and apply it to cosmic shear. Using analytical formulae for the non-linear matter power spectrum and bispectrum, we model iζ ± and validate it on N-body simulations within the uncertainties expected from the sixth year cosmic shear data of the Dark Energy Survey. We also explore the Fisher information content of iζ ± and perform a joint analysis with ξ ± for two tomographic source redshift bins with realistic shape-noise to analyse its power in constraining cosmological parameters. We find that the joint analysis of ξ ± and iζ ± has the potential to considerably improve parameter constraints from ξ ± alone, and can be particularly useful in improving the figure of merit of the dynamical dark energy equation of state parameters from cosmic shear data.

Joint analysis of anisotropic power spectrum, bispectrum and trispectrum: application to N-body simulations

“…Also in weak-lensing analyses the three-point correlation function and the bispectrum have been widely studied in the literature since the first seminal works [51][52][53]. More recent works focused on determining their added constraining potential with respect to two-point statistics [33,[54][55][56][57][58], together with application on data [59].…”

Weak lensing constraints on dark matter-baryon interactions with 𝖭-body simulations and machine learning

“…Besides two-point correlation functions, the analysis of higher-order statistics that contain cosmological information beyond that captured by two-point correlation functions, may further improve the limits of the cross-section [63][64][65][66][67][68][69]. This can be an interesting avenue to explore in future works.…”

The integrated angular bispectrum of weak lensing

“…If we shift the focus purely on maximizing sensitivity, rather than on testing accuracy, then a higher signal-to-noise for the integrated signal can likely be achieved by picking less squeezed triangles ( 3 ∼ 100), as the lensing signal is larger on smaller scales. During the reviewing process of this work, it was indeed shown in [41] that a fully flatsky approach using many extremely small patches is also possible and measures a strong non-Gaussian signal without probing precisely the large-scale modes on which we focus in this paper. For the reasons just mentioned, we find the two approaches complementary and addressing different questions.…”