Oscillatory behavior of closed isotropic models in second order gravity theory

TL;DR

This paper investigates the late-time oscillatory behavior of closed isotropic cosmological models within second order gravity theory using dynamical systems analysis, revealing conditions for periodic solutions and oscillations.

Contribution

It demonstrates that closed isotropic models in second order gravity can exhibit oscillatory behavior due to periodic solutions in the dynamical system.

Findings

Normal form analysis reveals periodic solutions for many initial conditions.

Oscillatory behavior can occur in initially expanding closed universes.

Late-time evolution shows potential for cyclic cosmological models.

Abstract

Homogeneous and isotropic models are studied in the Jordan frame of the second order gravity theory. The late time evolution of the models is analysed with the methods of the dynamical systems. The normal form of the dynamical system has periodic solutions for a large set of initial conditions. This implies that an initially expanding closed isotropic universe may exhibit oscillatory behaviour.