Expanding universes in the conformal frame of $f(R) $ gravity

TL;DR

This paper analyzes the late-time behavior of FRW cosmological models in $f(R)$ gravity's conformal frame, demonstrating stability of certain equilibria and energy transfer dynamics depending on matter properties and scalar potential minima.

Contribution

It provides a comprehensive stability analysis of cosmological solutions with arbitrary non-negative scalar potentials in $f(R)$ gravity's conformal frame, extending previous results.

Findings

Equilibria at non-negative local minima of $V$ are asymptotically stable.

For $ ext{gamma} > 1$, energy transfers from fluid to scalar field, leading to scalar field dominance.

Results hold for a broad class of potentials without specific asymptotic assumptions.

Abstract

The late time evolution of Friedmann-Robertson-Walker (FRW) models with a perfect fluid matter source is studied in the conformal frame of $f(R) $ gravity. We assume that the corresponding scalar field, nonminimally coupled to matter, has an arbitrary non-negative potential function $V(\phi) $. We prove that equilibria corresponding to non-negative local minima for $V$ are asymptotically stable. We investigate all cases where one of the matter components eventually dominates. 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 $\gamma $, 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.