2003ApJ...592..664P

Weak gravitational lensing provides a direct statistical measure of dark matter distribution. The variance is easiest to measure, which constrains the degenerate product σ₈Ω^0.6₀. The degeneracy is broken by measuring the skewness arising from the fact that densities must remain positive, which is not possible when the initially symmetric perturbations become nonlinear. Skewness measures the nonlinear mass scale, which in combination with the variance measures Ω₀directly. We present the first detection of dark matter skewness from the VIRMOS-DESCART survey. We have measured the full three-point function and its projections onto windowed skewness. We separate the lensing mode and the B-mode. The lensing skewness is detected for a compensated Gaussian on scales of 5'.37 to be κ{d1}³=1.06±0.06x10^–6. The B-modes are consistent with zero at this scale. The variance for the same window function is κ{d1}²=5.32±0.62±0.98x10^–5, resulting in S₃=375⁺³⁴²_–124. Comparing with N-body simulations, we find Ω₀<0.5 at 90% confidence. The Canada-France-Hawaii Telescope legacy survey and newer simulations should be able to improve significantly on the constraint.