Detection of Dark Matter Skewness in the VIRMOS‐DESCART Survey: Implications for Ω0

Weak gravitational lensing provides a direct statistical measure of the darkmatter distribution. The variance is easiest to measure, which constrains thedegenerate product \sigma_8\Omega^0.6. The degeneracy is broken by measuringthe skewness arising from the fact that densities must remain positive, whichis not possible when the initially symmetric perturbations become non-linear.Skewness measures the non-linear mass scale, which in combination with thevariance measures \Omega directly. We present the first detection of darkmatter skewness from the Virmos-Decart survey. We have measured the full threepoint function, and its projections onto windowed skewness. We separate thelensing mode and the B mode. The lensing skewness is detected for a compensatedGaussian on scales of 5.37 arc minutes to be \kappa^3=1.06+/-0.06x10^-6. TheB-modes are consistent with zero at this scale. The variance for the samewindow function is \kappa^2= 5.32+/-0.62+/-0.98x10^-5, resulting inS_3=375^{+342}_{-124}. Comparing to N-body simulations, we find \Omega_0<0.5 at90% confidence. The Canada-France-Hawaii-Telescope legacy survey and newersimulations should be able to improve significantly on the constraint.Comment: 26 pages 8 figures, accepted by ApJ, minor revisions, corrected eqn (21