2002A&A...393..369V

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 Ω_M, the mass power spectrum normalisation σ₈, the shape parameter Γ and the redshift of the sources z_s. Constraints on Ω_M and σ₈ (resp. Γ and z_s) are provided by marginalising over Γ and z_s ( resp. Ω_M and σ₈). For a flat ΛCDM cosmologies, using a photometric redshift prior for the sources and Γ∈[0.1,0.4], we find σ₈=(0.57±0.04)*Ω_M^{[(0.24±0.18)Ω}M_-0.49]^ at the 68% confidence level (the error budget includes statistical noise, full cosmic variance and residual systematics). The estimate of Γ, marginalised over Ω_M∈[0.1,0.4], σ₈∈[0.7,1.3] and z_s constrained by photometric redshifts, gives Γ=0.25±0.13 at 68% confidence. Adopting h=0.7, a flat universe, Γ=0.2 and Ω_m=0.3 we find σ₈=0.98±0.06. Combined with CMB measurements, our results suggest a non-zero cosmological constant and provide tight constraints on Ω_M and σ₈. Finally, we 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 in improving this.