Brane Models with a Ricci-Coupled Scalar Field

TL;DR

This paper derives exact and numerical solutions for a Ricci-coupled scalar field in brane models, exploring various geometries, scalar profiles, and graviton localization, revealing conditions for finite geometries and graviton trapping.

Contribution

It provides new exact and numerical solutions for scalar fields coupled to gravity in brane models, including thick branes and graviton localization analysis.

Findings

Finite geometries with exponential warp factors are achievable.

Scalar field solutions include folded-kink profiles in Randall-Sundrum geometry.

Graviton potential develops a local maximum at high coupling values.

Abstract

We consider the problem of a scalar field, non-minimally coupled to gravity through a $-\xi\phi^{2}R$ term, in the presence of a Brane. Exact solutions, for a wide range of values of the coupling parameter $\xi$, for both $\phi$-dependent and $\phi$-independent Brane tension, are derived and their behaviour is studied. In the case of a Randall-Sundrum geometry, a class of the resulting scalar field solutions exhibits a folded-kink profile. We go beyond the Randall-Sundrum geometry studying general warp factor solutions in the presence of a kink scalar. Analytic and numerical results are provided for the case of a Brane or for smooth geometries, where the scalar field acts as a thick Brane. It is shown that finite geometries with warp factors that asymptotically decrease exponentially are realizable for a wide range of parameter values. We also study graviton localization in our setup and find that the localizing potential for gravitons with the characteristic volcano-like profile develops a local maximum located at the origin for high values of the coupling $\xi$.