Dynamical system approach of non-minimal coupling in AdS/CFT cosmology

TL;DR

This paper investigates the cosmological dynamics of a non-minimally coupled scalar field within the AdS/CFT framework, deriving modified equations and analyzing attractor solutions for different couplings.

Contribution

It introduces a dynamical system approach to non-minimal coupling in AdS/CFT cosmology, exploring stability and attractor solutions for various coupling functions.

Findings

Past de Sitter attractor for minimal coupling

Future de Sitter attractor for conformal and non-minimal couplings

Modified Friedmann equations derived for the model

Abstract

We study the dynamical system approach of non minimally coupled scalar field to induced gravity on the brane in the framework of the AdS/CFT correspondence. In this context, we derive the modified Friedmann equation and the equation of motion. The dynamics of this model are studied by rewriting the cosmological field equations in the form of a system of autonomous differential equations. In particular, the analysis is considered by investigating an exponential potential and a monomial form of the non minimal coupling function. We show that, for sufficient conditions, a past de Sitter attractor solution is obtained in the case of a minimal coupling, meanwhile a future de Sitter attractor solutions is obtained for a conformal coupling and for a non minimal coupling.