Constraining dark energy evolution with gravitational lensing by large scale structures

We study the sensitivity of weak lensing by large scale structures as a probe of the evolution of dark energy. We explore a two-parameters model of dark energy evolution, inspired by tracking quintessence models. To this end, we compute the likelihood of a few fiducial models with varying and nonvarying equation of states. For the different models, we investigate the dark energy parameter degeneracies with the mass power spectrum shape $\ensuremath{\Gamma}$, normalization ${\ensuremath{\sigma}}_{8}$, and with the matter mean density ${\ensuremath{\Omega}}_{M}$. We find that degeneracies are such that weak lensing turns out to be a good probe of dark energy evolution, even with limited knowledge on $\ensuremath{\Gamma}$, ${\ensuremath{\sigma}}_{8}$, and ${\ensuremath{\Omega}}_{M}$. This result is a strong motivation for performing large scale structure simulations beyond the simple constant dark energy models, in order to calibrate the nonlinear regime accurately. Such calibration could then be used for any large scale structure tests of dark energy evolution. Prospective for the Canada France Hawaii Telescope Legacy Survey and Super-Novae Acceleration Probe are given. These results complement nicely the cosmic microwave background and supernovae constraints.