Expanding universes with scalar fields coupled to matter Roberto Giambò

We study the late time evolution of flat and negatively curved FriedmannRobertson-Walker (FRW) models with a perfect fluid matter source and a nonminimally coupled scalar field having an arbitrary non-negative potential function V (φ). We prove using the methods of dynamical systems, that equilibria corresponding to non-negative local minima for V are asymptotically stable. We classify all cases of the flat model where one of the matter components eventually dominate. The results are valid for a large class of non-negative potentials without any particular assumptions about the behavior of the potential at infinity. In particular for a nondegenerate minimum of the potential with zero critical value we show that if γ, the parameter of the equation of state is larger than one, then there is a transfer of energy from the fluid to the scalar field and the later eventually dominates in a generic way.