2007A&A...463..405S

Dark energy can be investigated in two complementary ways, by considering either general parameterizations or physically well-defined models. Following the second route, we explore the observational constraints on quintessence models where the acceleration of our universe is driven by a slow-rolling scalar field. Using weak lensing data to investigate high-energy motivated models of dark energy for the first time, the analysis focuses on cosmic shear, examining how weak lensing surveys can constrain dark energy, discussing the limitations due to the lack of knowledge of the non-linear regime, and combining with type Ia supernovae data and cosmic microwave background observations to lift some degeneracies. Using a Boltzmann code that includes quintessence models along with a weak lensing add-on code, we determine the shear power spectrum and several two-point statistics, describing the non-linear regime by two different mappings. The likelihood analysis completing the pipeline, based on a grid method, uses the ``gold set'' of supernovae Ia, VIRMOS-Descart and CFHTLS-deep and -wide data for weak lensing; we also explore larger angular scales, using a synthetic realization of the complete CFHTLS-wide survey, as well as of space-based mission surveys. WMAP-first year data are used for the normalization and to broadly define the location of the first acoustic peak constraining the quintessence parameter space. Two classes of cosmological parameters are discussed: i) those accounting for quintessence affect mainly geometrical factors; ii) cosmological parameters specifying the primordial universe strongly depend on the description of the non-linear regime. This dependence is confirmed using wide surveys, by discarding the smaller angular scales to reduce the dependence on the non-linear regime. For a flat universe and a quintessence inverse-power-law potential with slope α, the joint analysis gives α<1 and Ω_Q0=0.75^+0.03_–0.04 at a 95% confidence level, whereas α=2⁺¹⁸_–2, Ω_Q0=0.74^+0.03_–0.05 when including supergravity corrections.