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

TL;DR

This paper analyzes the late-time behavior of flat and negatively curved FRW cosmological models with a scalar field coupled to matter, demonstrating stability and energy transfer dynamics under certain potential conditions.

Contribution

It provides a stability analysis of equilibria in scalar field cosmologies within $f(R)$ theories and classifies matter dominance scenarios in flat models.

Findings

Equilibria with non-negative minima of V are asymptotically stable.

Energy transfer from matter to scalar field occurs when the equation of state parameter exceeds one.

Scalar field eventually dominates in models with a nondegenerate minimum of V at zero critical value.

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.