COSMOLOGICAL MODEL PREDICTIONS FOR WEAK LENSING - LINEAR AND NONLINEAR REGIMES

Weak lensing by large-scale structure induces correlated ellipticities in the images of distant galaxies. The two-point correlation is deter mined by the matter power spectrum along the line of sight. We use the fully nonlinear evolution of the power spectrum to compute the predic ted ellipticity correlation. We present results for different measures of the second moment for angular scales theta similar or equal to 1'- 3 degrees 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 amplitu de of ellipticity within a 15' radius is similar or equal to 0.001z(s) (0.6), almost independent of the cosmological model, with z(s) being t he median redshift of background galaxies. Nonlinear effects in the ev olution of the power spectrum significantly enhance the ellipticity fo r theta < 10'-for theta similar or equal to 1' the rms ellipticity is similar or equal to 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' < theta < 2 degrees, unlike the expectation from linear theory that the signal- to-noise ratio is strongly peaked on degree scales. The scaling with c osmological parameters also changes because of nonlinear effects. By m easuring the correlations on small (nonlinear) and large (linear) angu lar scales, different cosmological parameters can be independently con strained to obtain a model-independent estimate of both power spectrum amplitude and matter density Omega(m). Nonlinear effects also modify the probability distribution of the ellipticity. Using second-order pe rturbation theory, we find that over most of the range of interest the re are significant deviations from a normal distribution.