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In the generalized Randall-Sundrum warped brane-world model the cosmological constant induced on the visible brane can be positive or negative. In this paper we investigate profiles of vacuum expectation value of the bulk scalar field under general Dirichlet and Neumann boundary conditions in the generalized warped brane-world model. We show that the VEV profiles generally depend on the value of the brane cosmological constant. We find that the VEV profiles of the bulk scalar field for a visible brane with negative cosmological constant and positive tension are quite distinct from those of Randall-Sundrum model. In addition we show that the VEV profiles for a visible brane with large positive cosmological constant are also different from those of the Randall-Sundrum model. We also verify that Goldberger and Wise mechanism can work under nonzero Dirichlet boundary conditions in the generalized Randall-Sundrum model.

Extra dimension is an important subject in the realm of theoretical physics that provides many creative ways to solve some problems in physics such as hierarchy problem. Unlike the model of Arkani-Hamed et al. [

In the original RS model the cosmological constant induced on the visible brane is zero and the brane tension is negative. This model has been generalized such that the cosmological constant on the brane as well as brane tension can be positive or negative [

Recently, GW mechanism of radius stabilization in the brane-world model with nonzero brane cosmological constant has been considered [

The motivation for the present study is to study the VEV profile of the scalar field, including a brane cosmological constant and with different combinations of Dirichlet and Neumann boundary conditions at the two branes. We also want to know if this scalar can stabilize the size of the warped extra dimension. We note that the present accelerating phase of the universe is due to the presence of small positive cosmological constant with a tiny value of

This paper is organized as follows. In Section

One of the many different possibilities that can be explored to solve the hierarchy problem is Randall-Sundrum (RS) model [

The action of a bulk scalar field,

With the above warp factor equation of motion for the classical field can be written down:

For the positive induced brane cosmological constant

In this section, we study the VEV profiles of the bulk scalar field in a case without brane localized scalar potential in the generalized Randall-Sundrum model. By utilizing (

We discuss a case in which both boundary conditions on the

In Figure

The VEV profile under

For dS brane,

In Figure

The dependence of VEV profile under

In

Next, we consider the

Finally, we investigate the

In this section we studied the VEV profile of a bulk scalar field under four boundary conditions on a generalized warped brane-world model in the absence of brane localized potential. We found that the VEV profiles depend on the vanishingly small brane cosmological constant.

In this section, we formulate the VEV profiles of the bulk scalar field in a case with brane localized scalar potentials in the generalized Randall-Sundrum model. The action of a bulk field in the presence of brane potentials reads as

For some other choices of the brane potentials see [

Here, we consider the

When the boundary quartic coupling is finite, the numerical calculation indicates that

The VEV profile for negative induced brane cosmological constant with positive brane tension for

For the

The VEV profile for large positive brane cosmological constant with

The

The VEV profile for negative induced brane cosmological constant with positive brane tension for

Recently, this mechanism was studied in the generalized warped brane models with a nonzero brane cosmological constant by [

We have investigated the unknown coefficients

In the generalized warped model as mentioned in [

In the RS model a negative tension visible brane is utilized to describe our Universe. However, such negative tension branes are unstable. Hence in this work we considered a generalized RS warped model.

In this paper, we investigated a bulk scalar field under Dirichlet and Neumann boundary conditions in a generalized RS warped model with a nonzero cosmological constant on the brane. First we have obtained the profiles of VEV of the bulk scalar in the absence of brane localized potential for the negative and positive brane cosmological constant. We find the following.

For an AdS visible brane with negative brane tension the results are similar to RS case.

However for an AdS visible brane with positive brane tension the results are different from the RS case. In this case the VEV profile undergoes sudden changes near the IR brane. Moreover we see that the IR brane is displaced from its RS location. The coefficients

For a dS visible brane the results for small values of

We have also verified GW mechanism in the generalized RS model with Dirichlet and Neumann boundary conditions. Analogous to RS model [

Our analysis of consistent boundary conditions is similar to that of Csáki et al. [

There are quantum corrections from Casimir effect and induced gravity on the brane. One requires that the brane-world metric be a solution of the quantum-corrected Einstein equations. For the RS model this issue has been addressed in [

In the analysis presented in this work we have ignored the backreaction of the scalar field on the space-time geometry. The stress tensor for the scalar field in the limit of large modulus can be obtained [

In this work our choices for the bulk and the brane potentials were those of [

In a previous work we studied the case of a scalar field nonminimally coupled to the Ricci curvature scalar [

In the RS [

The situation is different in the generalized Randall-Sundrum model.

This subject is discussed in [

If we denote

Next we will show below in this situation that the brane tension of the visible brane is positive. As far as the stability of the brane is concerned this is a desirable feature. To compute the brane tension

But for the minus sign case the brane tension for the visible brane is positive and it is given as

When the cosmological constant of the brane is positive we have

The authors declare that there is no conflict of interests regarding the publication of this paper.