How Sensitive Are Weak Lensing Statistics to Dark Energy Content?

Future weak lensing surveys will directly probe the clustering of dark matter, in addition to providing a test for various cosmological models. Recent studies have provided us with the tools which can be used to construct the complete probability distribution function for convergence fields. It is also possible to construct the bias associated with the hot-spots in convergence maps. These techniques can be used in both the quasi-linear and the highly nonlinear regimes using various well developed numerical methods. We use these results here to study the weak lensing statistics of cosmological models with dark energy. We study how well various classes of dark energy models can be distinguished from models with a cosmological constant. We find that the ratio of the square root of the variance of convergence is complementary to the convergence skewness $S_3$ in probing dark energy equation of state; it can be used to predict the expected difference in weak lensing statistics between various dark energy models, and for choosing optimized smoothing angles to constrain a given class of dark energy models. Our results should be useful for probing dark energy using future weak lensing data with high statistics from galaxy weak lensing surveys and supernova pencil beam surveys.