Non-Gaussian statistics in galaxy weak lensing: compressed three-point correlations and cosmological forecasts

TL;DR

This work quantifies how much cosmological information is contained in non-Gaussian statistics of galaxy weak lensing via the 3PCF. It uses a harmonic decomposition into multipoles, PCA compression, and DALI forecasting, validated against 108 full-sky simulations, plus a Gaussian analytic covariance. The key finding is that only the first few multipoles carry most information, and adding the 3PCF to the 2PCF improves constraints on Omega_m and sigma8 by about 20%, with redshift-dependent gains for S8 and w0. The study provides practical guidance for upcoming surveys and delivers a public code for computing and compressing the 3PCF of weak-lensing convergence.

Abstract

Building on previous developments of a harmonic decomposition framework for computing the three-point correlation function (3PCF) of projected scalar fields over the sky, this work investigates how much cosmological information is contained in these higher-order statistics. We perform a forecast to determine the number of harmonic multipoles required to capture the full information content of the 3PCF in the context of galaxy weak lensing, finding that only the first few multipoles are sufficient to capture the additional cosmological information provided by the 3PCF. This study addresses a critical practical question: to what extent can the high-dimensional 3PCF signal be compressed without significant loss of cosmological information? Since the different multipoles contain highly redundant information, we apply a principal component analysis (PCA) which further reduces its dimensionality and preserving information. We also account for non-linear parameter degeneracies using the DALI method, an extension of Fisher forecasting that includes higher-order likelihood information. Under optimistic settings, we find that the 3PCF considerably improves the constraining power of the 2PCF for $Ω_m$, reaching a 20% improvement. Other parameters also benefit, mainly due to their degeneracy with the matter abundance. For example, with our chosen scale cuts for galaxy sources at $z = 0.5$, we find that $σ_8$ is more tightly constrained, whereas $S_8$ and $w_0$ are not. Finally, we construct analytical Gaussian covariance matrices that can serve as a first step toward developing semi-analytical, semi-empirical alternatives to sample covariances.

Figures (11)

• Figure 1: $\zeta_m(\theta_1,\theta_2)$ bins used in this work for a single multipole. The space marked with a checkmark show the bins for which our analytical modeling is within $1\sigma$ of the simulated data in the cases $m=0,1,2,3$.
• Figure 2: Top panel: Comparison of model and data vectors. The blue lines show the relative difference between the two, while the shaded region indicates the 1$\sigma$ uncertainty derived from the simulated data. The final model vector (black curves) is constructed using the bins marked with a check in \ref{['fig:zetam_bins']}. Bottom panel: We show only the data vector used (black dashed lines) and compared to the model vector (solid lines). However, we extend the multipoles up to $m=5$. The shadowing shows the 1$\sigma$ errors. For visualization purposes, we have multiplied $\xi$ by $1/2000$.
• Figure 3: Sample covariance matrix (left panel) and correlation matrix (right panel) for the data vector shown in \ref{['fig:datavector_all']} up to bin index = 153, corresponding to the 2PCF, $\xi$, and 3PCF multipoles $\zeta_{m=0,1,2}$. Although throughout this work we use multipoles up to $m=8$, we only show $m=0,1,2$ to avoid cluttering.
• Figure 4: Fisher forecast over the $(\Omega_m, \sigma_8)$ parameter space when the multipoles from $\zeta_{m=0}$ to $\zeta_{m=8}$ are analyzed separately. The left and center panels show the $1\sigma$ errors on $\Omega_m$ and $\sigma_8$, respectively, while the right panel shows the FoM. This plot shows the quadrupole is the multipole providing the most restrictive constraints, with $\sqrt{{\rm FoM}}=66.69$. For comparison, the value for square root of the FoM for the 2PCF is 118.71.
• Figure 5: Left panel: 1 and 2 $\sigma$ confidence contours on parameter space $(\Omega_m,\sigma_8)$, provided by forecasting with Fisher (black-dashed curves) and DALI (green contours). Right panel: forecasts on the space of parameters $(\Omega_m,S_8)$, where $S_8$ is computed from the chains obtained using DALI (green contours) and using Fisher (black dashed curves). We also show in the dot-dashed blue curves the contour obtained by transforming the Fisher matrix with the linear relation in \ref{['FisherLT']}. In both panels we have used the quadrupole of the 3PCF for the galaxy distribution centered at redshift $z=0.5$.