# Towards generic cosmological evolution without singularity and fundamental symmetry of space-time

## TL;DR

This paper explores a cosmological model with a non-minimally coupled scalar field using dynamical systems, identifying conditions for an unstable de Sitter state linked to conformal coupling in higher-dimensional gravity theories.

## Contribution

It introduces a dynamical systems approach to analyze cosmological models with non-minimal coupling, highlighting the role of the coupling constant in the stability of de Sitter states.

## Key findings

- Unstable de Sitter state exists for specific coupling constants
- Conformal coupling in higher dimensions relates to instability
- Provides insights into non-singular cosmological evolution

## Abstract

Dynamical systems methods are used to investigate cosmological model with non-minimally coupled scalar field. Existence of an asymptotically unstable de Sitter state distinguishes values of the non-minimal coupling constant parameter $\frac{3}{16}\le\xi<\frac{1}{4}$, which correspond to conformal coupling in higher dimensional theories of gravity.