Energy exchange for homogeneous and isotropic universes with a scalar field coupled to matter

Abstract

We study the late time evolution of flat and negatively curved Friedmann-Robertson-Walker (FRW) models with a perfect fluid matter source and a scalar field arising in the conformal frame of $f(R)$ theories nonminimally coupled to matter. Under mild assumptions on the potential V we prove that equilibria corresponding to non-negative local minima for V are asymptotically stable, as well as horizontal asymptotes approached from above by V. We classify all cases of the flat model where one of the matter components eventually dominates. In particular for a nondegenerate minimum of the potential with zero critical value we prove in detail that if 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.

18 pages, LaTeX, 1 figure

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