The recollapse problem of closed FRW models in higher-order gravity theories

TL;DR

This paper investigates whether closed FRW universes in higher-order gravity theories inevitably recollapse, analyzing the dynamics with scalar fields and matter, and exploring conditions that might prevent recollapse.

Contribution

It extends previous analysis by including matter and applies dynamical systems methods to study recollapse in higher-order gravity models.

Findings

Initially expanding closed universes cannot avoid recollapse if starting near Minkowski spacetime.

Potential with a positive minimum may prevent the recollapse of closed universes.

The structure of the dynamical system reveals conditions for recollapse or avoidance.

Abstract

We study the closed universe recollapse conjecture for positively curved FRW models with a perfect fluid matter source and a scalar field which arises in the conformal frame of the $R+\alpha R^{2}$ theory. By including ordinary matter, we extend the analysis of a previous work. We analyze the structure of the resulted four-dimensional dynamical system with the methods of the center manifold theory and the normal form theory. It is shown that an initially expanding closed FRW universe, starting close to the Minkowski spacetime, cannot avoid recollapse. We discuss the posibility that potentials with a positive minimum may prevent the recollapse of closed universes.