We present a maximum likelihood analysis of cosmological parameters from measurements of the aperture mass up to 35 arcmin , using simulated and real cosmic shear data .
A four-dimensional parameter space is explored which examines the mean density \Omega _ { M } , the mass power spectrum normalization \sigma _ { 8 } , the shape parameter \Gamma and the redshift of the sources z _ { s } .
Constraints on \Omega _ { M } and \sigma _ { 8 } ( resp . \Gamma and z _ { s } ) are then given by marginalizing over \Gamma and z _ { s } ( resp . \Omega _ { M } and \sigma _ { 8 } ) .
For a flat \Lambda CDM cosmologies , using a photometric redshift prior for the sources and \Gamma \in [ 0.1 , 0.4 ] , we find \sigma _ { 8 } = \left ( 0.57 \pm 0.04 \right ) \Omega _ { M } ^ { \left ( 0.24 \mp 0.18 \right ) % \Omega _ { M } -0.49 } at the 68 \% confidence level ( the error budget includes statistical noise , full cosmic variance and residual systematic ) .
The estimate of \Gamma , marginalized over \Omega _ { M } \in [ 0.1 , 0.4 ] , \sigma _ { 8 } \in [ 0.7 , 1.3 ] and z _ { s } constrained by photometric redshifts , gives \Gamma = 0.25 \pm 0.13 at 68 \% confidence .
Adopting h = 0.7 , a flat universe , \Gamma = 0.2 and \Omega _ { m } = 0.3 we find \sigma _ { 8 } =0.98 \pm 0.06 .
Combined with CMB , our results suggest a non-zero cosmological constant and provide tight constraints on \Omega _ { M } and \sigma _ { 8 } .
We finaly compare our results to the cluster abundance ones , and discuss the possible discrepancy with the latest determinations of the cluster method .
In particular we point out the actual limitations of the mass power spectrum prediction in the non-linear regime , and the importance for its improvement .