Cosmic shear statistics and cosmology*

We report a measurement of cosmic shear correlations using an effective area of 6.5 deg2of the VIRMOS deep imaging survey in progress at the Canada-France-Hawaii Telescope. We measured various shear correlation functions, the aperture mass statistic and the top-hat smoothed variance of the shear with a detection significance exceeding $12 \sigma$. We present results on angular scales from 3 arcsec to half a degree. The lensing origin of the signal is confirmed through tests that rely on the scalar nature of the gravitational potential. The different statistical measures give consistent results over the full range of angular scales. These important tests of the measurements demonstrate that the measured correlations could provide accurate constraints on cosmological parameters, subject to the systematic uncertainty in the source redshift distribution. The measurement over more than two decades of scale allows one to evaluate the effect of the shape of the power spectrum on cosmological parameter estimation. The degeneracy on $\sigma_8-\Omega_0$can be broken if priors on the shape of the linear power spectrum (parameterized by Γ) are assumed. For instance, with $\Gamma=0.21$and at the $95\%$confidence level, we obtain $0.65< \sigma_8< 1.2$and $0.22< \Omega_0< 0.55$for open models, and $\sigma_8> 0.7$and $\Omega_0< 0.4$for flat (Λ-CDM) models. We discuss how these results would scale if the assumed source redshift distribution needed to be modified with forthcoming measurements of photometric redshifts. From the tangential/radial mode decomposition we can set an upper limit on the intrinsic shape alignment, which has recently been suggested as a possible contribution to the lensing signal. Within the error bars, there is no detection of intrinsic shape alignment for scales larger than $1'$.