CFHTLenS tomographic weak lensing: quantifying accurate redshift distributions

The Canada-France-Hawaii Telescope Lensing Survey (CFHTLenS) comprises deep multi-colour (u*g'r'i'z') photometry spanning 154 deg(2), with accurate photometric redshifts and shape measurements. We demonstrate that the redshift probability distribution function summed over galaxies provides an accurate representation of the galaxy redshift distribution accounting for random and catastrophic errors for galaxies with best-fitting photometric redshifts z(p) < 1.3. We present cosmological constraints using tomographic weak gravitational lensing by large-scale structure. We use two broad redshift bins 0.5 < z(p) <= 0.85 and 0.85 < z(p) <= 1.3 free of intrinsic alignment contamination, and measure the shear correlation function on angular scales in the range similar to 1-40 arcmin. We show that the problematic redshift scaling of the shear signal, found in previous Canada-France-Hawaii Telescope Legacy Survey data analyses, does not affect the CFHTLenS data. For a flat Lambda cold dark matter model and a fixed matter density Omega(m) = 0.27, we find the normalization of the matter power spectrum sigma(8) = 0.771 +/- 0.041. When combined with cosmic microwave background data (Wilkinson Microwave Anisotropy Probe 7-year results), baryon acoustic oscillation data (BOSS) and a prior on the Hubble constant from the Hubble Space Telescope distance ladder, we find that CFHTLenS improves the precision of the fully marginalized parameter estimates by an average factor of 1.5-2. Combining our results with the above cosmological probes, we find Omega(m) = 0.2762 +/- 0.0074 and sigma(8) = 0.802 +/- 0.013.