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 CFHTLenS and combine those
with CMB anisotropy probes. The third moment is measured with a significance of
$2\sigma$. The combined constraint on $\Sigma_8 = \sigma_8 (\Omega_{\rm
m}/0.27)^\alpha$ is improved by 10%, in comparison to the second-order only,
and the allowed ranges for $\Omega_{\rm m}$ 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
$\Omega_{\rm m}$ and $\sigma_8$ by 26% for flat $\Lambda$CDM. For a model with
free curvature, the joint CFHTLenS-Planck result is $\Omega_{\rm m} = 0.28 \pm
0.02$ (68% confidence), which is an improvement of 43% 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 nonlinear model and
the Gaussianity of the likelihood function.
