Weak lensing and dark energy: The impact of dark energy on nonlinear dark matter clustering

We examine the influence of percent-level dark energy corrections to the nonlinear matter power spectrum on constraints of the dark energy equation of state from future weak lensing probes. We explicitly show that a poor approximation (off by greater than or similar to 10%) to the nonlinear corrections causes a greater than or similar to 1 sigma bias on the determination of the dark energy equation of state. Future weak lensing surveys must therefore incorporate dark energy modifications to the nonlinear matter power spectrum accurate to the percent-level, to avoid introducing significant bias in their measurements. For the WMAP5 cosmology, the more accurate power spectrum is more sensitive to dark energy properties, resulting in a factor of 2 improvement in dark energy equation of state constraints. We explore the complementary constraints on dark energy from future weak lensing and supernova surveys. A space-based, Joint Dark Energy Mission-like survey measures the equation of state in five independent redshift bins to similar to 10%, while this improves to similar to 5% for a wide-field ground-based survey like the Large Synoptic Survey Telescope. These constraints are contingent upon our ability to control weak lensing systematic uncertainties to the sub-percent level.