CFHTLenS: cosmological constraints from a combination of cosmic shear two-point and three-point correlations

Higher order, non-Gaussian aspects of the large-scale structure carry valuable information on structure formation and cosmology, which is complementary to second-order statistics. In this work, we measure second- and third-order weak-lensing aperture-mass moments from the Canada-France-Hawaii Lensing Survey (CFHTLenS) and combine those with cosmic microwave background (CMB) anisotropy probes. The third moment is measured with a significance of 2 sigma. The combined constraint on I (8) pound = sigma(8)(Omega(m)/0.27)(alpha) is improved by 10 per cent, in comparison to the second-order only, and the allowed ranges for Omega(m) and sigma(8) are substantially reduced. Including general triangles of the lensing bispectrum yields tighter constraints compared to probing mainly equilateral triangles. Second- and third-order CFHTLenS lensing measurements improve Planck CMB constraints on Omega(m) and sigma(8) by 26 per cent for flat I > cold dark matter. For a model with free curvature, the joint CFHTLenS-Planck result is Omega(m) = 0.28 +/- 0.02 (68 per cent confidence), which is an improvement of 43 per cent compared to Planck alone. We test how our results are potentially subject to three astrophysical sources of contamination: source-lens clustering, the intrinsic alignment of galaxy shapes, and baryonic effects. We explore future limitations of the cosmological use of third-order weak lensing, such as the non-linear model and the Gaussianity of the likelihood function.