I will present how the EUCLID satellite will improve our knowledge in the cosmic parameters, in the languages of traditional error bars, figure of merit (FOM), and Shannon entropy information. In this talk I will focus on early-Universe inflation and dark energy models. We show that for many early-Universe inflation models EUCLID can be an essential experiment, with an improvement of a factor of about 10 in the FOM of inflationary parameters, with respect to Planck-only CMB constraint. For dark energy the $w_0-w_a$ FOM can be improved by a factor of about 30 (or about 5 bits in Shannon entropy), with respect to present-day constraint. We explain, for the first time, why the phenomenological $w_0-w_a$ FOM can be used as a generic measure, by showing that it is approximately equivalent to a physical FOM for a wide class of quintessence models.

IPhT CEA-Saclay