Optimization of ESPRESSO Fundamental Physics Tests

ESPRESSO is a high-resolution-ultra-stable spectrograph for the VLT, whose commissioning is expected in late 2016. One of its key science drivers is to test the stability of fundamental couplings such as the fine structure constant with unprecedent accuracy and control of possible systematics. The criteria for selecting an optimal target list for the Consortium's GTO is an ongoing work and the present forecasts of the impact that this sample will have on fundamental physics and cosmology is discussed. In particular, we discuss how these measurements and future supernova datasets will constrain the behaviour of dark energy deep in the matter era (i.e., in the redshift range 1.5 .; (ordered from largest to smallest) and the variance of the new parameters, al = l/>.;. We consider models for which the variation of a is linearly proportional to the displacement of a scalar field, and further assume that this field is a quintessence type field, i.e. responsible