Likelihood Analysis of Cosmic Shear on Simulated and VIRMOS-DESCART Data

We present a maximum likelihood analysis of cosmological parameters from measurements of the aperture mass up to 35 arcmin, using simulated and real cosmic shear data. A four-dimensional parameter space is explored which examines the mean density \Omega_M, the mass power spectrum normalization \sigma_8, the shape parameter \Gamma and the redshift of the sources z_s. Constraints on \Omega_M and \sigma_8 (resp. \Gamma and z_s) are then given by marginalizing over \Gamma and z_s (resp. \Omega_M and \sigma_8). For a flat LCDM cosmologies, using a photometric redshift prior for the sources and \Gamma \in [0.1,0.4], we find \sigma_8=(0.57\pm0.04) \Omega_M^{(0.24\mp 0.18) \Omega_M-0.49} at the 68% confidence level (the error budget includes statistical noise, full cosmic variance and residual systematic). The estimate of \Gamma, marginalized over \Omega_M \in [0.1,0.4], \sigma_8 \in [0.7,1.3] and z_s constrained by photometric redshifts, gives \Gamma=0.25\pm 0.13 at 68% confidence. Adopting h=0.7, a flat universe, \Gamma=0.2 and \Omega_m=0.3 we find \sigma_8=0.98 \pm0.06 . Combined with CMB, our results suggest a non-zero cosmological constant and provide tight constraints on \Omega_M and \sigma_8. We finaly compare our results to the cluster abundance ones, and discuss the possible discrepancy with the latest determinations of the cluster method. In particular we point out the actual limitations of the mass power spectrum prediction in the non-linear regime, and the importance for its improvement.