Weighing the Cosmological Energy Contents with Weak Gravitational Lensing

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Abstract
Using perturbation theory, Bernardeau, Van Waerbeke, & Mellier show that the skewness of the large-scale lensing convergence, or projected mass density, could be used to constrain Ωm, the matter content of the universe. However, deep weak-lensing field surveys in the near future will likely measure the convergence on small angular scales (10'), where the signal will be dominated by highly nonlinear fluctuations. We develop a method for computing the small-scale convergence skewness that gives predictions that agree well with existing results from ray-tracing N-body simulations but is significantly faster. We demonstrate that the small-scale convergence skewness is insensitive to the shape and normalization of the primordial (cold dark matter-type) power spectrum, making it dependent almost entirely on the cosmological energy contents. Moreover, nonlinear clustering appears to enhance the differences between predictions of the convergence skewness for a range of models. Hence, in addition to constraining Ωm, the small-scale convergence skewness from future deep and several degrees wide surveys can be used to differentiate between curvature-dominated and cosmological constant (Λ)-dominated models, as well as to constrain the equation of state of a quintessence component, thereby distinguishing Λ from quintessence. Finally, our method can be easily generalized to other measures such as the aperture mass statistics.
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