Higher-order Convergence Statistics for Three-dimensional Weak Gravitational Lensing

TL;DR

This paper develops analytical tools for higher-order statistics like bispectrum and trispectrum in 3D weak gravitational lensing, aiming to improve constraints on dark matter and dark energy by utilizing tomographic data.

Contribution

It introduces analytical expressions for higher-order lensing statistics and their power spectra, extending beyond the power spectrum to better probe cosmological parameters.

Findings

Derived analytical formulas for bispectrum and trispectrum in 3D lensing.

Analyzed redshift dependence and noise effects on these higher-order statistics.

Demonstrated potential for improved cosmological constraints with future surveys.

Abstract

Weak gravitational lensing on a cosmological scales can provide strong constraints both on the nature of dark matter and the dark energy equation of state. Most current weak lensing studies are restricted to (two-dimensional) projections, but tomographic studies with photometric redshifts have started, and future surveys offer the possibility of probing the evolution of structure with redshift. In future we will be able to probe the growth of structure in 3D and put tighter constraints on cosmological models than can be achieved by the use of galaxy redshift surveys alone. Earlier studies in this direction focused mainly on evolution of the 3D power spectrum, but extension to higher-order statistics can lift degeneracies as well as providing information on primordial non-gaussianity. We present analytical results for specific higher-order descriptors, the bispectrum and trispectrum, as well as collapsed multi-point statistics derived from them, i.e. cumulant correlators. We also compute quantities we call the power spectra associated with the bispectrum and trispectrum, the Fourier transforms of the well-known cumulant correlators. We compute the redshift dependence of these objects and study their performance in the presence of realistic noise and photometric redshift errors.