Efficiency of weak lensing surveys to probe cosmological models

We apply a mass reconstruction technique to large-scale structure gravitational distortion maps, simulated for different cosmological scenarii on scales from 2.5 arcmin to 10 degrees. The projected mass is reconstructed using a non-parametric least square method involving the reduced shear on which noise due to intrinsic galaxy ellipticities has been added. The distortion of the galaxies is calculated using the full lens equation, without any hypothesis like the weak lensing approximation, or other linearization. It is shown that the noise in the reconstructed maps is perfectly uncorrelated Poissonian, with no propagation from short to large scales. The measured power spectrum and first four moments of the convergence can be corrected accurately for this source of noise. The cosmic variance of these quantities is then analyzed with respect to the density of the background galaxies using 60 realizations of each model. We show that a moderately deep weak lensing survey (5 × 5 degrees with a typical background population of 30 gal/arcmin² at a redshift z_s ≃ 1) is able to probe the amplitude of the power spectrum with a few percent accuracy for models with σ₈ Ω^0.8 = 0.6. Remarkably, we have found that, using the third moment of the local convergence only, such a survey would lead to a 6 σ separation between open (Ω = 0.3) and flat (Ω = 1) models. This separation does not require a very deep survey, and it is shown to be robust against different hypothesis for the normalization or the shape of the power spectrum. Finally, the observational strategy for an optimal measurement of the power spectrum and the moments of the convergence is discussed.