Uniting cosmological epochs through the twister solution in cosmology with non-minimal coupling

TL;DR

This paper explores a unified cosmological model using a non-minimally coupled scalar field, revealing a twister solution that connects all major universe epochs without assuming specific scalar potential forms.

Contribution

It introduces a generic dynamical system approach to cosmology with non-minimal coupling, identifying critical points representing key universe epochs and discovering a twister solution linking them.

Findings

Identified fixed points for all major universe epochs.

Found that inflation, radiation, and matter epochs are transient.

Discovered a twister solution connecting all critical points.

Abstract

We investigate dynamics of a flat FRW cosmological model with a barotropic matter and a non-minimally coupled scalar field (both canonical and phantom). In our approach we do not assume any specific form of a potential function for the scalar field and we are looking for generic scenarios of evolution. We show that dynamics of universe can be reduced to a 3-dimensional dynamical system. We have found the set of fixed points and established their character. These critical points represent all important epochs in evolution of the universe : (a) a finite scale factor singularity, (b) an inflation (rapid-roll and slow-roll), (c) a radiation domination, (d) a matter domination and (e) a quintessence era. We have shown that the inflation, the radiation and matter domination epochs are transient ones and last for a finite amount of time. The existence of the radiation domination epoch is purely the effect of a non-minimal coupling constant. We show the existence of a twister type solution wandering between all these critical points.