Second Randall-Sundrum brane world scenario with a nonminimally coupled bulk scalar field

Abstract

In our previous work of Ref. [5] we studied the stability of the RS2-model with a nonminimally coupled bulk scalar field φ, and we found that in appropriate regions of ξ the standard RS2-vacuum becomes unstable. The question that arises is whether there exist other new static stable solutions where the system can relax. In this work, by solving numerically the Einstein equations with the appropriate boundary conditions on the brane, we find that depending on the value of the nonminimal coupling ξ, this model possesses three classes of new static solutions with different characteristics. We also examine what happens when the fine tuning of the RS2-model is violated, and we obtain that these three classes of solutions are preserved in appropriate regions of the parameter space of the problem. The stability properties and possible physical implications of these new solutions are discussed in the main part of this paper. Especially in the case where ξ = ξ c (ξ c is the five dimensional conformal coupling) and the fine tuning is violated, we obtain a physically interesting static stable solution.

Gauss-Bonnet gravity, brane world models, and nonminimal coupling

“…Thus, we will restrict our study to the classes of numerical solutions we obtained in [9]. We aim to investigate how Gauss-Bonnet gravity affects these solutions.…”

“…[9], exhibit a naked singularity (in particular the warp factor becomes zero in finite proper distance in the bulk), while the scalar field tends to infinity near the singularity.…”

“…[9], by solving numerically the Einstein equations in the case of a non-minimally coupled scalar field, we have obtained three classes of static solutions with different features, in appropriate regions of the free parameters of the model. The numerical approach we apply in [9] is suitable for the general case of the potential. However, we have focused to the case of a massless scalar field assuming the simplest generally accepted form of the potential: V (φ) = λφ…”

“…The motivation is to examine how Gauss-Bonnet gravity affects the three classes of solutions we obtained in our previous work [9].…”

“…[9,10] we have studied brane world models with a bulk scalar field non-minimally coupled with gravity, via a possible interaction term of the form −1/2ξRφ 2 . Our motivation was to construct brane models which incorporate a layer-phase mechanism [11,12,13,14] for the localization of the ordinary particles on the brane.…”