Likelihood Analysis of Cosmic Shear on Simulated and VIRMOS-DESCART Data

Abstract

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 normalization σ_8, the shape parameter Γand the redshift of the sources z_s. Constraints on Ω_M and σ_8 (resp. Γand z_s) are then given by marginalizing over Γand z_s (resp. Ω_M and σ_8). For a flat LCDM cosmologies, using a photometric redshift prior for the sources and Γ\in [0.1,0.4], we find σ_8=(0.57\pm0.04) Ω_M^{(0.24\mp 0.18) Ω_M-0.49} at the 68% confidence level (the error budget includes statistical noise, full cosmic variance and residual systematic). The estimate of Γ, marginalized over Ω_M \in [0.1,0.4], σ_8 \in [0.7,1.3] and z_s constrained by photometric redshifts, gives Γ=0.25\pm 0.13 at 68% confidence. Adopting h=0.7, a flat universe, Γ=0.2 and Ω_m=0.3 we find σ_8=0.98 \pm0.06 . Combined with CMB, our results suggest a non-zero cosmological constant and provide tight constraints on Ω_M and σ_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.