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 normalisation sigma(8), the shape parameter and the redshift of the sources z(s). Constraints on Omega(M) and sigma(8) (resp. Gamma and z(s)) are provided by marginalising over Gamma and z(s) (resp. Omega(M) and sigma(8)). For a flat LambdaCDM cosmologies, using a photometric redshift prior for the sources and Gamma is an element of [0.1; 0.4], we find sigma(8) = (0.57 +/- 0.04) Omega(M)((0.24-/+0.18)OmegaM-0.49) at the 68% confidence level (the error budget includes statistical noise, full cosmic variance and residual systematics). The estimate of Gamma, marginalised over Omega(M) is an element of [0.1; 0.4], sigma(8) is an element of [0.7; 1.3] and z(s) constrained by photometric redshifts, gives Gamma = 0.25 +/- 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 +/- 0.06. Combined with CMB measurements, our results suggest a non-zero cosmological constant and provide tight constraints on Omega(M) and sigma(8). Finally, we 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 in improving this.