INTEGRABLE MULTIDIMENSIONAL COSMOLOGIES WITH MATTER AND A SCALAR FIELD

The thesis discusses some integrable (i.e., explicitly solvable) cosmologies à la Robertson -Walker, with possibly non zero spatial curvature. In these models, the content of the universe consists of matter and of a scalar field. The expression "matter" is used in a broad sense, and includes as a special case the radiation; the considered matter has pressure p_m and density ϱ_m, related by an equation of state p_m = w ϱ_m, with w an arbitrary constant (w = 0 in the case of dust; w = 1/d in the case of a radiation gas). The scalar field is used as a model for the dark energy content of the universe, refining the standard cosmological constant model. (We recall the denomination of "quintessence", often used for a scalar field with this rôle.)