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 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.

Some remarks about non-minimally coupled scalar field models

“…It is easy to note that the model arising from the action (8) can be obtained from (1) with the choice χ(φ) = e √ 2/3φ . Thus, the results in [161] and in [168] can be obtained as particular cases by investigating a general class of models containing both STTs and F (R) gravity.…”

“…For completeness let's show our Proposition 3 in [170], which is an extension of the Proposition 1 of [168] for flat FLRW models since we have included radiation. This proposition gives a characterization of the future attractor of the system (12) under some mild assumptions for the potential.…”

“…which decays more faster to zero than the function W (φ, y, ρ m , H) = −ka −2 , k = −1, 0 defined in [168] as a → +∞. (The complete proof is offered in [170]).…”

“…e.g., in [168,169,170,171,162]. In [168] were investigated flat and negatively curved FLRW models with a perfect fluid matter source and a nonminimally coupled scalar field φ with potential V (φ) (related to the F (R) function).…”

“…The aim of the paper is to extent several results in [155,156,161,168,169,171,91] for the general case of arbitrary potentials and arbitrary couplings. It is described the early and late-time dynamics of the models and we pay special attention to the possible scaling solutions.…”