Theoretical wavelet ℓ₁-norm from one-point probability density function prediction

¹ Université Paris-Saclay, Université Paris Cité, CEA, CNRS, AIM, 91191 Gif-sur-Yvette, France
² Universitäts-Sternwarte, Fakultät für Physik, Ludwig-Maximilians-Universität München, Scheinerstraße 1, 81679 München, Germany
³ Institutes of Computer Science and Astrophysics, Foundation for Research and Technology Hellas (FORTH), Heraklion, Crete, Greece

^★ Corresponding author; vilasini.tinnanerisreekanth@cea.fr

Received: 21 March 2024
Accepted: 19 August 2024

Abstract

Context. Weak gravitational lensing, which results from the bending of light by matter along the line of sight, is a potent tool for exploring large-scale structures, particularly in quantifying non-Gaussianities. It is a pivotal objective for upcoming surveys. In the realm of current and forthcoming full-sky weak-lensing surveys, convergence maps, which represent a line-of-sight integration of the matter density field up to the source redshift, facilitate field-level inference. This provides an advantageous avenue for cosmological exploration. Traditional two-point statistics fall short of capturing non-Gaussianities, necessitating the use of higher-order statistics to extract this crucial information. Among the various available higher-order statistics, the wavelet ℓ₁ -norm has proven its efficiency in inferring cosmology. However, the lack of a robust theoretical framework mandates reliance on simulations, which demand substantial resources and time.

Aims. Our novel approach introduces a theoretical prediction of the wavelet ℓ₁-norm for weak-lensing convergence maps that is grounded in the principles of large-deviation theory. This method builds upon recent work and offers a theoretical prescription for an aperture mass one-point probability density function.

Methods. We present for the first time a theoretical prediction of the wavelet ℓ₁-norm for convergence maps that is derived from the theoretical prediction of their one-point probability distribution. Additionally, we explored the cosmological dependence of this prediction and validated the results on simulations.

Results. A comparison of our predicted wavelet ℓ₁ -norm with simulations demonstrates a high level of accuracy in the weakly nonlinear regime. Moreover, we show its ability to capture cosmological dependence. This paves the way for a more robust and efficient parameter-inference process.