Constraining Dark Energy Evolution with Gravitational Lensing by Large Scale Structures

We study the sensitivity of weak lensing by large scale structures to the evolution of dark energy. We explore a 2-parameters model of dark energy evolution, inspired by tracking quintessence models. To this end, we compute the likelihood of a few representative models with varying and non varying equation of states. Based on an earlier work, we show that the evolution of dark energy has a much stronger impact on the non-linear structure growth than on the angular diameter distance, which makes large scale structure measurements a very efficient probe of this evolution. For the different models, we investigate the dark energy parameters degeneracies with the mass power spectrum shape Gamma, normalisation sigma_8, and with the matter mean density 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 non-linear regime accurately. Prospective for the Canada France Hawaii Telescope Legacy Survey (CFHTLS) and Super-Novae Acceleration Probe (SNAP) are given. These results complement nicely the cosmic microwave background and Super-Novae constraints. Weak lensing is shown to be more sensitive to a variation of the equation of state, whereas CMB and SNIa give information on its constant part.