  We present a finely-binned tomographic weak lensing analysis of the
Canada-France-Hawaii Telescope Lensing Survey, CFHTLenS, mitigating
contamination to the signal from the presence of intrinsic galaxy alignments
via the simultaneous fit of a cosmological model and an intrinsic alignment
model. CFHTLenS spans 154 square degrees in five optical bands, with accurate
shear and photometric redshifts for a galaxy sample with a median redshift of
zm =0.70. We estimate the 21 sets of cosmic shear correlation functions
associated with six redshift bins, each spanning the angular range of
1.5<theta<35 arcmin. We combine this CFHTLenS data with auxiliary cosmological
probes: the cosmic microwave background with data from WMAP7, baryon acoustic
oscillations with data from BOSS, and a prior on the Hubble constant from the
HST distance ladder. This leads to constraints on the normalisation of the
matter power spectrum sigma_8 = 0.799 +/- 0.015 and the matter density
parameter Omega_m = 0.271 +/- 0.010 for a flat Lambda CDM cosmology. For a flat
wCDM cosmology we constrain the dark energy equation of state parameter w =
-1.02 +/- 0.09. We also provide constraints for curved Lambda CDM and wCDM
cosmologies. We find the intrinsic alignment contamination to be galaxy-type
dependent with a significant intrinsic alignment signal found for early-type
galaxies, in contrast to the late-type galaxy sample for which the intrinsic
alignment signal is found to be consistent with zero.
