Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Thick brane in Palatini formalism with a non-minimally coupled bulk scalar field

Tahereh Azizi, Mojtaba Alimoradi

TL;DR

This work develops a stable thick brane in five-dimensional Palatini gravity with a bulk scalar non-minimally coupled to the Ricci scalar, deriving the modified field equations and constructing analytic solutions for a flat 4D geometry and a kink-like scalar profile. By introducing an auxiliary metric and specific ansatzes, the authors obtain a bell-shaped warp factor, a symmetric volcano-like potential, and a regular energy density, indicating a finite-thickness brane. Linear tensor perturbations yield a Schrödinger-like equation that factorizes into a supersymmetric form, guaranteeing the absence of tachyonic modes and enabling localization of the graviton zero mode on the brane, while the KK spectrum shows increasing delocalization of massive modes. The results demonstrate gravity localization within the Palatini framework and highlight distinctions from metric-based approaches, offering a foundation for further phenomenological explorations, including fermion localization and gravitational-wave tests.

Abstract

We study a thick brane scenario within the Palatini formulation of gravity, where the metric and affine connection are treated as independent variables. By introducing a non-minimal coupling between a bulk scalar field and the Ricci scalar, we obtain analytic solutions under a flat, four-dimensional Poincaré-invariant metric with a kink-like scalar configuration. The warp factor exhibits a bell-shaped profile, while the scalar potential forms a symmetric volcano-like structure, characteristic of a finite-thickness brane. The corresponding energy density is regular and localized, featuring a central peak with symmetrically placed negative minima. Through the analysis of linear tensor perturbations, we derive a Schrödinger-like equation with supersymmetric factorization, ensuring the absence of tachyonic modes and thus the stability of the background configuration. The effective potential also takes a volcano-like form that supports a localized graviton zero mode, confirming the recovery of four-dimensional gravity on the brane. A numerical study of the massive Kaluza--Klein spectrum reveals the progressive delocalization of massive modes into the bulk. Our results demonstrate a stable and physically consistent thick brane configuration within the Palatini gravity framework, offering new insights into gravity localization and braneworld phenomenology.

Thick brane in Palatini formalism with a non-minimally coupled bulk scalar field

TL;DR

This work develops a stable thick brane in five-dimensional Palatini gravity with a bulk scalar non-minimally coupled to the Ricci scalar, deriving the modified field equations and constructing analytic solutions for a flat 4D geometry and a kink-like scalar profile. By introducing an auxiliary metric and specific ansatzes, the authors obtain a bell-shaped warp factor, a symmetric volcano-like potential, and a regular energy density, indicating a finite-thickness brane. Linear tensor perturbations yield a Schrödinger-like equation that factorizes into a supersymmetric form, guaranteeing the absence of tachyonic modes and enabling localization of the graviton zero mode on the brane, while the KK spectrum shows increasing delocalization of massive modes. The results demonstrate gravity localization within the Palatini framework and highlight distinctions from metric-based approaches, offering a foundation for further phenomenological explorations, including fermion localization and gravitational-wave tests.

Abstract

We study a thick brane scenario within the Palatini formulation of gravity, where the metric and affine connection are treated as independent variables. By introducing a non-minimal coupling between a bulk scalar field and the Ricci scalar, we obtain analytic solutions under a flat, four-dimensional Poincaré-invariant metric with a kink-like scalar configuration. The warp factor exhibits a bell-shaped profile, while the scalar potential forms a symmetric volcano-like structure, characteristic of a finite-thickness brane. The corresponding energy density is regular and localized, featuring a central peak with symmetrically placed negative minima. Through the analysis of linear tensor perturbations, we derive a Schrödinger-like equation with supersymmetric factorization, ensuring the absence of tachyonic modes and thus the stability of the background configuration. The effective potential also takes a volcano-like form that supports a localized graviton zero mode, confirming the recovery of four-dimensional gravity on the brane. A numerical study of the massive Kaluza--Klein spectrum reveals the progressive delocalization of massive modes into the bulk. Our results demonstrate a stable and physically consistent thick brane configuration within the Palatini gravity framework, offering new insights into gravity localization and braneworld phenomenology.
Paper Structure (4 sections, 42 equations, 7 figures)

This paper contains 4 sections, 42 equations, 7 figures.

Table of Contents

  1. Introduction
  2. The model and the solution
  3. Linear stability and the localization of gravity
  4. Discussions and Conclusion

Figures (7)

  • Figure 1: The scalar field $\phi(y)$ versus $y$ for different values of $b$.
  • Figure 2: The shape of the warp factor associated to the function in Eq.(\ref{['warp']}) versus the extra dimension $y$ for various values of $n$ (a) and the coupling parameter $\xi$ (b). The parameters are set to $b =c= 1$.
  • Figure 3: Potential of scalar field (a) and energy density (b) depicted as a function of extra dimension for $b =c= 1$ and $n = \xi=0.9$.
  • Figure 4: The potential with respect to $\phi$. The numerical values are the same as figure \ref{['pot-rho']}
  • Figure 5: Plotting of gravitational zero mode $\psi_0(z)$ versus the conformal coordinate $z$ for $n=0.9$.
  • ...and 2 more figures