(De)Stabilization of an extra dimension due to a Casimir force

Abstract

We study the stabilization of one spatial dimension in (p+1+1)-dimensional spacetime in the presence of $p$-dimensional brane(s), a bulk cosmological constant and the Casimir force generated by a conformally coupled scalar field. We find general static solutions to the metric which require the fine-tuning of the inter-brane distance and the bulk cosmological constant (leaving the two brane tensions as free parameters) corresponding to a vanishing effective cosmological constant and a constant radion field. Taking these solutions as a background configuration, we perform a dimensional reduction and study the effective theory in the case of one- and two-brane configurations. We show that the radion field can have a positive mass squared, which corresponds to a stabilization of the extra dimension, only for a repulsive nature of the Casimir force. This type of solution requires the presence of a negative tension brane. The solutions with one or two positive tension branes arising in this theory turn out to have negative radion mass squared, and therefore are not stable.

new references added, version published in PRD

Cited by in corpus (68)

• Cosmological and black hole brane-world Universes in higher derivative gravity
• Casimir effect in de Sitter and Anti-de Sitter braneworlds
• The Casimir Effect on Background of Conformally Flat Brane--World Geometries
• The Casimir Effect in the Presence of a Minimal Length
• KK Parity in Warped Extra Dimension
• Surface Casimir densities and induced cosmological constant in higher dimensional braneworlds
• Wightman function and Casimir densities on AdS bulk with application to the Randall-Sundrum braneworld
• A 6-D Brane World Model
• The Casimir Effect in the Presence of Compactified Universal Extra Dimensions
• A small weak scale from a small cosmological constant
• Heat trace asymptotics with transmittal boundary conditions and quantum brane-world scenario
• Casimir energy for de Sitter branes in bulk AdS(5)
• Stress-energy tensor for a quantised bulk scalar field in the Randall-Sundrum brane model
• The Casimir Force in Randall Sundrum Models
• Wightman function and vacuum fluctuations in higher dimensional brane models
• The Casimir Force in Randall Sundrum Models with q+1 dimensions
• A more attractive scheme for radion stabilization and supercooled phase transition
• Quantum self-consistency of $AdS\times \Sigma$ brane models
• Vacuum Energy, the Cosmological Constant and Compact Extra Dimensions: Constraints from Casimir Effect Experiments
• Finite Temperature Casimir Effect in Kaluza-Klein Spacetime
• Finite temperature Casimir effect in spacetime with extra compactified dimensions
• Bulk quantum effects for de Sitter branes in AdS(5)
• Scalar heat kernel with boundary in the worldline formalism
• Higgs-Radion Mixing with Enhanced Di-Photon Signal
• Quintessence from Shape Moduli
• Warm intermediate inflation in the Randall-Sundrum II model in the light of Planck 2015 and BICEP2 results: A general dissipative coefficient
• Casimir Effect in Spacetime with Extra Dimensions -- From Kaluza-Klein to Randall-Sundrum Models
• Radius Stabilization by Two-Loop Casimir Energy
• On the Stabilization of the Size of Extra Dimensions
• Finite temperature Casimir effect for massive scalar field in spacetime with extra dimensions
• Second order perturbations in the radius stabilized Randall-Sundrum two branes model
• Quantum effects in five-dimensional brane-world: creation of deSitter branes and particles and stabilization of induced cosmological constant
• Bulk Scalar Stabilization of the Radion without Metric Back-Reaction in the Randall-Sundrum Model
• Multiple Hierarchies from a Warped Extra Dimension
• Can thick braneworlds be self-consistent?
• Stable, Time-Dependent, Exact Solutions for Brane Models with a Bulk Scalar Field
• Casimir Energy and Brane Stability
• Casimir dynamics: Interactions of Surfaces with codimension >1 due to Quantum Fluctuations
• Casimir effect between anti-de Sitter braneworlds
• String versus Einstein frame in an AdS/CFT induced quantum dilatonic brane-world universe
• Traces on orbifolds: Anomalies and one-loop amplitudes
• Wightman function and vacuum densities for a Z_2-symmetric thick brane in AdS spacetime
• Radion Stabilization by Brane Matter
• Neutrino Dark Energy and Moduli Stabilization in a BPS Braneworld Scenario
• Warped Geometry in Higher Dimensions with an Orbifold Extra Dimension
• The one-loop vacuum energy and RG flow induced by double-trace operators in AdS/CFT and dS/CFT correspondence
• Dynamical generation of fermion mass hierarchy in an extra dimension
• One-loop effective potential from higher-dimensional AdS black holes
• Casimir Effect, Achucarro-Ortiz Black Hole and the Cosmological Constant
• Radion and moduli stabilization from induced brane actions in higher-dimensional brane worlds
• Casimir Energies due to Matter Fields in $T^2$ and $T^2/Z_2$ Compactifications
• The Shape of Compact Toroidal Dimensions $T_{\theta }^d$ and the Casimir Effect on $M^D\times T_{\theta }^d$ spacetime
• Electromagnetic Casimir piston in higher dimensional spacetimes
• Second order perturbations in the radius stabilized Randall-Sundrum two branes model II -- Effect of relaxing strong coupling approximation --
• Radiative stabilization of warped space
• Ghosts and Tachyons in the Fifth Dimension
• Radion and Higgs masses in gauge-Higgs unification
• Revisiting Vacuum Energy in Compact Spacetimes
• Dynamical generation of quark/lepton mass hierarchy in an extra dimension
• Braneworlds and Dark Energy
• Investigation into Compactified Dimensions: Casimir Energies and Phenomenological Aspects
• Comments on conformal stability of brane-world models
• Vacuum densities for a thick brane in AdS spacetime
• Conformal matter in warped backgrounds
• On The Problem of Vacuum energy in Brane Theories
• The Zeta Function Approach to Casimir Energy Calculations in Higher Dimensions
• Non-constant ground states for symmetry-breaking fields in brane world models
• Casimir energy and the possibility of higher dimensional manipulation