Cosmological Model Predictions for Weak Lensing: Linear and Nonlinear Regimes

Abstract

Weak lensing by large-scale structure induces correlated ellipticities in the images of distant galaxies. The two-point correlation is determined by the matter power spectrum along the line of sight. We use the fully nonlinear evolution of the power spectrum to compute the predicted ellipticity correlation. We present results for different measures of the second moment for angular scales θ ≃ 1'-3° and for alternative normalizations of the power spectrum, in order to explore the best strategy for constraining the cosmological parameters. Normalizing to observed cluster abundance, the rms amplitude of ellipticity within a 15' radius is ≃0.01 z s 0.6 , almost independent of the cosmological model, with z s being the median redshift of background galaxies. Nonlinear effects in the evolution of the power spectrum significantly enhance the ellipticity for θ < 10'—for θ ≃ 1' the rms ellipticity is ≃0.05, which is nearly twice as large as the linear prediction. This enhancement means that the signal-to-noise ratio for the ellipticity is only weakly increasing with angle for 2' < θ < 2°, unlike the expectation from linear theory that the signal-to-noise ratio is strongly peaked on degree scales. The scaling with cosmological parameters also changes because of nonlinear effects. By measuring the correlations on small (nonlinear) and large (linear) angular scales, different cosmological parameters can be independently constrained to obtain a model-independent estimate of both power spectrum amplitude and matter density Ω m . Nonlinear effects also modify the probability distribution of the ellipticity. Using second-order perturbation theory, we find that over most of the range of interest there are significant deviations from a normal distribution.