We use weak lensing data from the Hubble Space Telescope COSMOS survey to measure the second- and third-moments of the cosmic shear field , estimated from about 450 000 galaxies with average redshift \bar { z } \sim 1.3 .

We measure two- and three-point shear statistics using a tree-code , dividing the signal in E , B and mixed components .
We present a detection of the third-order moment of the aperture mass statistic and verify that the measurement is robust against systematic errors caused by point spread function ( PSF ) residuals and by the intrinsic alignments between galaxies .
The amplitude of the measured three-point cosmic shear signal is in very good agreement with the predictions for a WMAP7 best-fit model , whereas the amplitudes of potential systematics are consistent with zero .

We make use of three sets of large { \Lambda CDM } simulations to test the accuracy of the cosmological predictions and to estimate the influence of the cosmology-dependent covariance .

We perform a likelihood analysis using the measurement of \langle M _ { ap } ^ { 3 } \rangle ( \theta ) and find that the \Omega _ { m } - \sigma _ { 8 } degeneracy direction is well fitted by the relation : \sigma _ { 8 } ( \Omega _ { m } / 0.30 ) ^ { 0.49 } = 0.78 ^ { +0.11 } _ { -0.26 } which is in good agreement with the best fit relation obtained by using the measurement of \langle M _ { ap } ^ { 2 } \rangle ( \theta ) : \sigma _ { 8 } ( \Omega _ { m } / 0.30 ) ^ { 0.67 } = 0.70 ^ { +0.11 } _ { -0.14 } .

We present the first measurement of the more generalised three-point shear statistic \langle M _ { ap } ^ { 3 } \rangle ( \theta _ { 1 } , \theta _ { 2 } , \theta _ { 3 } ) and find a very good agreement with the WMAP7 best-fit cosmology .
The cosmological interpretation of \langle M _ { ap } ^ { 3 } \rangle ( \theta _ { 1 } , \theta _ { 2 } , \theta _ { 3 } ) gives \sigma _ { 8 } ( \Omega _ { m } / 0.30 ) ^ { 0.46 } = 0.69 ^ { +0.08 } _ { -0.14 } .
Furthermore , the combined likelihood analysis of \langle M _ { ap } ^ { 3 } \rangle ( \theta _ { 1 } , \theta _ { 2 } , \theta _ { 3 } ) and \langle M _ { ap } ^ { 2 } \rangle ( \theta ) improves the accuracy of the cosmological constraints to \sigma _ { 8 } ( \Omega _ { m } / 0.30 ) ^ { 0.50 } = 0.69 ^ { +0.07 } _ { -0.12 } , showing the high potential of this combination of measurements to infer cosmological constraints .