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

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.

arXiv comment19 pages, 7 figures

References in corpus (47)

• A Large Mass Hierarchy from a Small Extra Dimension
• An Alternative to Compactification
• The Hierarchy Problem and New Dimensions at a Millimeter
• 4D Gravity on a Brane in 5D Minkowski Space
• Modeling the fifth dimension with scalars and gravity
• Kaluza-Klein Gravity
• Brane-world gravity
• Palatini Approach to Modified Gravity: f(R) Theories and Beyond
• Universal Aspects of Gravity Localized on Thick Branes
• Four-dimensional gravity on a thick domain wall
• Inflation with Non-Minimal Coupling: Metric vs. Palatini Formulations
• Brane World Cosmology
• Thick brane solutions
• Thick Brane Worlds and Their Stability
• Thick domain walls and singular spaces
• Braneworld Models of Scalar Fields with Generalized Dynamics
• Localization of 4D gravity on pure geometrical Thick branes
• Localization of Matters on Pure Geometrical Thick Branes
• Domain wall brane in squared curvature gravity
• Observational constraints on braneworld inflation: the effect of a Gauss-Bonnet term
• Tensor perturbations of $f(R)$-branes
• Localization of bulk matter fields, the hierarchy problem and corrections to Coulomb's law on a pure de Sitter thick braneworld
• Thick branes with a nonminimally coupled bulk-scalar field
• Palatini frames in scalar-tensor theories of gravity
• Thick brane models in generalized theories of gravity
• Pure geometric thick $f(R)$-branes: stability and localization of gravity
• Thick brane in $f(R)$ gravity with Palatini dynamics
• Scalar perturbations from brane-world inflation
• De Sitter brane-world, localization of gravity, and the cosmological constant
• Gravity-induced instability and gauge field localization
• DGP Cosmology with a Non-Minimally Coupled Scalar Field on the Brane
• The structure of $f(R)$-brane model
• Thick brane structures in generalized hybrid metric-Palatini gravity
• Non-minimal Coupling Branes
• A new extended quintessence
• Tensor perturbations of Palatini $f(\mathcal{R})$-branes
• Stable Palatini $f(\mathcal{R})$ braneworld
• Natural Braneworld Inflation in Light of Recent Results from Planck and BICEP2
• On the stability of thick brane worlds non-minimally coupled to gravity
• Observational Constraints on the Normal Branch of a Warped DGP Cosmology
• Localization of scalar field on the brane-world by coupling with gravity
• Phantom-like effects in asymmetric brane embedding with induced gravity and the Gauss-Bonnet term in the Bulk
• Probing extra dimensions through cosmological observations of dark energy
• Pure geometric $f(R)$ branes
• Cosmology of a Friedmann-Lamaître-Robertson-Walker 3-brane, Late-Time Cosmic Acceleration, and the Cosmic Coincidence
• Thick branes via higher order field theory models with exponential and power-law tails
• Thick brane models in generalized mimetic gravity