Note on Warped Compactification -- Finite Brane Potentials and Non-Hermiticity --

Abstract

We study radius stabilization in the Randall-Sundrum model without assuming any unnaturally large stabilizing scalar potential parameter at the boundary branes ($\gamma$) by the frequently used superpotential method. Employing a perturbative expansion in $1/{\gamma }^2$ and the backreaction parameter, we obtain approximate analytical expressions for the radion mass and wavefunction. We validate them through a dedicated numerical analysis, which solves the linearized coupled scalar and metric field equations exactly. It is observed that the radion mass decreases with decreasing $\gamma$. Below a critical value of $\gamma$, the radion becomes tachyonic, suggesting destabilization of the extra dimension. We also address the issue of non-Hermiticity of the differential operator that determines the radion and Kaluza-Klein (KK) mode wavefunctions in the finite $\gamma$ limit. It is accomplished by finding an explicit form of the general scalar product that re-establishes the orthogonality in the KK decomposition.

23 pages, 2 figures, matches the published version

References in corpus (10)

• Gravitational Waves from Warped Spacetime
• QCD-induced Electroweak Phase Transition
• The Supercooled Universe
• Gravitational Backreaction Effects on the Holographic Phase Transition
• Cosmological Phase Transition of Spontaneous Confinement
• A more attractive scheme for radion stabilization and supercooled phase transition
• Phase Transitions from the Fifth Dimension
• Geometries with mismatched branes
• Multi-brane cosmology
• Confinement in de Sitter Space and the Swampland

Cited by in corpus (1)

• Wiggly dilaton: a landscape of spontaneously broken scale invariance