Breaking the Degeneracy: Optimal Use of Three-point Weak Lensing Statistics

Abstract

We study the optimal use of third order statistics in the analysis of weak lensing by large-scale structure. These higher order statistics have long been advocated as a powerful tool to break measured degeneracies between cosmological parameters. Using ray-tracing simulations, incorporating important survey features such as a realistic depth-dependent redshift distribution, we find that a joint two- and three-point correlation function analysis is a much stronger probe of cosmology than the skewness statistic. We compare different observing strategies, showing that for a limited survey time there is an optimal depth for the measurement of third-order statistics, which balances statistical noise and cosmic variance against signal amplitude. We find that the chosen CFHTLS observing strategy was optimal and forecast that a joint two- and three-point analysis of the completed CFHTLS-Wide will constrain the amplitude of the matter power spectrum $\sigma_8$ to 10% and the matter density parameter $\Omega_m$ to 17%, a factor of ~2.5 improvement on the two-point analysis alone. Our error analysis includes all non-Gaussian terms, finding that the coupling between cosmic variance and shot noise is a non-negligible contribution which should be included in any future analytical error calculations.