The integrated three-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 Map 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.

Response approach to the integrated shear 3-point correlation function: the impact of baryonic effects on small scales

“…Interestingly, we will also see that the addition of 𝜁 ± helps to tighten the constraints on the baryonic feedback parameters themselves, which strengthens the opportunity for cosmic shear data to constrain not only cosmology but also astrophysical models of AGN feedback (Huang et al 2021). This provides further motivation to include 𝜁 ± information in constraint analyses of cosmic shear data, reinforcing the promising potential of this statistic that Halder et al 2021 had highlighted before.…”

“…This semi-analytical approach takes as inputs the nonlinear matter power spectrum and its response functions to long-wavelength perturbations, which are much easier to predict and calibrate using 𝑁-body simulations compared to the full nonlinear matter bispectrum. One of our main results in this paper is the demonstration of the accuracy of the response approach to describe the integrated shear 3PCF 𝜁 ± (𝛼) deep in the 1 We drop the letter 𝑖 from the notation 𝑖𝜁 ± used in Halder et al 2021 to avoid confusion with the imaginary unit 𝑖 = √ −1. 2 This statistic was first introduced by Chiang et al (2014Chiang et al ( , 2015 in the context of three-dimensional galaxy clustering analyses, where it admits a similar physical interpretation.…”

“…Here, we focus our attention on a particularly promising way of accessing 3PCF information in the cosmic shear field using a statistic called the integrated shear 3-point correlation function 𝜁 ± (𝛼), which has been described recently 1 in Halder et al 2021 (see also Munshi et al (2021), and for studies of its harmonic counterpart we refer to Munshi et al (2020) and Jung et al (2021)). Concretely, 𝜁 ± (𝛼) describes the correlation between (i) the shear 2PCF measured locally inside well-defined patches on the sky, and (ii) the 1-point aperture shear mass of the patches.…”

“…As we will see below, the key theoretical ingredient to predict 𝜁 ± is the three-dimensional matter bispectrum 𝐵 3D 𝛿 ( 𝒌 1 , 𝒌 2 , 𝒌 3 ), where the 𝒌 𝑖 are wavevectors in Fourier space. In Halder et al 2021, this was calculated using the fitting function of Gil-Marín et al 2012, which was fitted only on scales 𝑘 0.4ℎ/Mpc, and as a result, it could not be used to describe the parts of 𝜁 ± that get contributions from the nonlinear regime of structure formation on smaller scales. In this paper, one of our goals is to remedy this by putting forward an alternative calculation of 𝜁 ± that is accurate on small scales, and that can therefore maximize the utility of this statistic to constrain cosmology.…”

Comparing weak lensing peak counts in baryonic correction models to hydrodynamical simulations

“…However, it has been found that these statistics do not capture all the information from the non-linear and non-Gaussian regime of the WL field. This has led to an array of work attempting to extract this additional information, including non-Gaussian 𝑁-point statistics such as the 3-point function and its Fourier transform the angular bispectrum (Fu et al 2014;Coulton et al 2019;Halder et al 2021;Halder & Barreira 2022), Minkowski functionals (Maturi et al 2010;Munshi et al 2011;Kratochvil et al 2012;Petri et al 2013;Marques et al 2019;Gatti et al 2021), convergence peak and minima statistics (Jain & Van Waerbeke 2000;Yang et al 2011;Liu et al 2015;Kacprzak et al 2016;Li et al 2019;Martinet et al 2021;Zürcher et al 2021;Harnois-Déraps et al 2021), as well as machine learning methods (Gupta et al 2018;Fluri et al 2019;Ribli et al 2019;Matilla et al 2020;) and related techniques (Cheng et al 2020).…”