Weak Lensing Statistics as a Probe of Omega and Power Spectrum

TL;DR

This paper investigates how weak lensing statistics, specifically the moments of the convergence field, depend on cosmological parameters and the power spectrum, proposing their joint use to measure these parameters from wide-field surveys.

Contribution

It provides a systematic analysis of the dependence of weak lensing moments on cosmological parameters and the power spectrum, highlighting the potential for parameter estimation.

Findings

Variance of convergence scales as P(k) Omega_0^{1.5} z_s^{1.5}

Skewness depends on Omega_0^{-0.8} z_s^{-1.35}

Joint analysis can constrain P(k) and Omega_0

Abstract

The possibility of detecting weak lensing effects from deep wide field imaging surveys has open new means of probing the large-scale structures of the Universe and measuring cosmological parameters. In this paper we present a systematic study of the expected dependence of the low order moments of the filtered gravitational local convergence with the power spectrum of the density fluctuations and with the cosmological parameters Omega_0 and Lambda. The results show a significant dependence with all these parameters. Though we note that this degeneracy could be partially raised by considering two populations of sources, at different redshifts, computing the third moment is more promising since it is expected, in the quasi-linear regime and for Gaussian initial conditions, to be only $\Omega_0$ dependent (with a slight degeneracy with Lambda) when it is correctly expressed in terms of the second moment. More precisely we show that the variance of the convergence varies approximately as P(k) Omega_0^{1.5} z_s^{1.5}, whereas the skewness varies as Omega_0^{-0.8} z_s^{-1.35}, where P(k) is the projected power spectrum and z_s the redshift of sources. Thus, used jointly they can provide both P(k) and Omega_0. However, the dependence with the redshift of sources is large and could be a major concern for a practical implementation. We have estimated the errors expected for these parameters in realistic scenario and sketched what would be the observational requirements for doing such measurements. A more detailed study of an observational strategy is left for a second paper.