Efficiency of weak lensing surveys to probe cosmological models

We apply a mass reconstruction technique to simulated large-scale structure gravitational distortion maps, from 2.5' to 10 degree scales, for different cosmological scenarii. The projected mass is reconstructed using a non-parametric least square method after noise due to the galaxy intrinsic ellipticities has been added on. The shearing of the galaxies is performed using the full lensing equation, without any hypothesis like the weak lensing approximation, or other linearization. It is shown that, in the reconstructed maps the noise acts as a perfect uncorrelated Poisson noise, with no propagation at large scales. The measured power spectrum and first four moments of the convergence can be corrected accurately for this source of noise. Using 60 realizations for each model, we show that a weak lensing survey of 5x5 degrees with a typical sheared background population of 30 gal/arcmin^2 at a redshift z_s=1, is able to probe the amplitude of the power spectrum with a few percents accuracy. Such a survey would lead to a 6 sigma separation between open (Omega=0.3) and flat (Omega=1) model. This separation is shown to be robust against different hypothesis for the normalization or the shape of the power spectrum, and does not require very deep surveys. The observational strategy for an optimal measurement of the power spectrum and the moments of the convergence is discussed.