Dealing with systematics in cosmic shear studies: new results from the VIRMOS-Descart Survey

We present a reanalysis of the VIRMOS-Descart weak lensing data, with a particular focus on different corrections for the variation of the point spread function anisotropy (PSF) across the CCDs. We show that the small scale systematics can be minimised, and eventually suppressed, using the B mode (curled shear component)measured in the corrected stars and galaxies. Updated cosmological constraints are obtained, free of systematics caused by PSF anisotropy. To facilitate general use of our results, we provide the two-points statistics data points with their covariance matrices up to a scale of one degree. For the normalisation of the mass power spectrum we obtain sigma_8=(0.83\pm 0.07)(Omega_M/0.3)^(-0.49). The shape parameter Gamma was marginalised over Gamma=[0.1,0.3] and the mean source redshift z_s over [0.8,1.0]. The latter is consistent with recent photometric redshifts obtained for the VIRMOS data and the preliminary spectroscopic redshifts from the VIRMOS-VVDS survey. The quoted 68% contour level includes all identified sources of error. We discuss the possible sources of residual contamination in this result: the effect of the non-linear mass power spectrum and remaining issues concerning the PSF correction. Our result is compared with the first release of the Wilkinson Microwave Anisotropy Probe data. It is found that Cold Dark Matter models with a power law primordial power spectrum and high matter density Omega_M > 0.5 are excluded at 3-sigma.