Very weak lensing in the CFHTLS wide:: cosmology from cosmic shear in the linear regime

Aims. We present an exploration of weak lensing by large-scale structure in the linear regime, using the third-year (T0003) CFHTLS Wide data release. Our results place tight constraints on the scaling of the amplitude of the matter power spectrum sigma(8) with the matter density Omega(m). Methods. Spanning 57 square degrees to i(AB)(') = 24.5 over three independent fields, the unprecedented contiguous area of this survey permits high signal-to-noise measurements of two-point shear statistics from 1 arcmin to 4 degrees. Understanding systematic errors in our analysis is vital in interpreting the results. We therefore demonstrate the percent-level accuracy of our method using STEP simulations, an E/B-mode decomposition of the data, and the star-galaxy cross correlation function. We also present a thorough analysis of the galaxy redshift distribution using redshift data from the CFHTLS T0003 Deep fields that probe the same spatial regions as the Wide fields. Results. We find sigma(8)(Omega(m)/0.25)(0.64) = 0.785 +/- 0.043 using the aperture-mass statistic for the full range of angular scales for an assumed flat cosmology, in excellent agreement with WMAP3 constraints. The largest physical scale probed by our analysis is 85 Mpc, assuming a mean redshift of lenses of 0.5 and a Lambda CDM cosmology. This allows for the first time to constrain cosmology using only cosmic shear measurements in the linear regime. Using only angular scales theta > 85 arcmin, we find sigma(8)(Omega(m)/0.25)(lin)(0.53) = 0.837 +/- 0.084, which agree with the results from our full analysis. Combining our results with data from WMAP3, we find. m = 0.248 +/- 0.019 and sigma(8) = 0.771 +/-0.029.