The non-minimal coupling constant and the primordial de Sitter state

TL;DR

This paper uses dynamical systems to analyze a cosmological model with a non-minimally coupled scalar field, identifying conditions for de Sitter states and their stability, which impacts early universe evolution without singularities.

Contribution

It reveals the special role of the conformal coupling constant in five dimensions and characterizes the stability of de Sitter states in such models.

Findings

De Sitter and Einstein-de Sitter states exist at infinite scalar field values.

De Sitter state is unstable for certain potential functions.

The model predicts a universe evolution without initial singularity.

Abstract

Dynamical systems methods are used to investigate dynamics of a flat Friedmann-Robertson-Walker cosmological model with the non-minimally coupled scalar field and a potential function. Performed analysis distinguishes the value of non-minimal coupling constant parameter $\xi=\frac{3}{16}$, which is the conformal coupling in five dimensional theory of gravity. It is shown that for a monomial potential functions at infinite values of the scalar field there exist generic de Sitter and Einstein-de Sitter states. The de Sitter state is unstable with respect to expansion of the Universe for potential functions which do not change faster than linearly. This leads to a generic cosmological evolution without the initial singularity.