Brane gravity, higher derivative terms and non-locality

Abstract

In brane world scenarios with a bulk scalar field between two branes it is known that 4-dimensional Einstein gravity is restored at low energies on either brane. By using a gauge-invariant gravitational and scalar perturbation formalism we extend the theory of weak gravity in the brane world scenarios to higher energies, or shorter distances. We argue that weak gravity on either brane is indistinguishable from 4-dimensional higher derivative gravity, provided that the inter-brane distance (radion) is stabilized, that the background bulk scalar field is changing near the branes and that the background bulk geometry near the branes is warped. This argument holds for a general conformal transformation to a frame in which matter on the branes is minimally coupled to the metric. In particular, Newton's constant and the coefficients of curvature-squared terms in the 4-dimensional effective action are determined up to an ambiguity of adding a Gauss-Bonnet topological term. In other words, we provide the brane-world realization of the so called $R^2$-model without utilizing a quantum theory. We discuss the appearance of composite spin-2 and spin-0 fields in addition to the graviton on the brane and point out a possibility that the spin-0 field may play the role of an effective inflaton to drive brane-world inflation. Finally, we conjecture that the sequence of higher derivative terms is an infinite series and, thus, indicates non-locality in the brane world scenarios.

Latex, 18 pages; a comment on the spurious tensor mode was added; recovery condition of higher derivative gravity clarified

References in corpus (4)

• Integro-differential equation for brane-world cosmological perturbations
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• Doubly covariant action principle of singular hypersurfaces in general relativity and scalar-tensor theories
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Cited by in corpus (19)

• Radion and Holographic Brane Gravity
• Brane World Effective Action at Low Energies and AdS/CFT Correspondence
• Low energy effective theory for two branes system
• Exact identification of the radion and its coupling to the observable sector
• Non-uniform Braneworld Stars: an Exact Solution
• On the quasi-linearity of the Einstein- "Gauss-Bonnet" gravity field equations
• Warped Flux Compactification and Brane Gravity
• Six-dimensional localized black holes: numerical solutions
• Nonlocal braneworld action: an alternative to Kaluza-Klein description
• Dynamical Stability of Six-dimensional Warped Flux Compactification
• Second order perturbations in the radius stabilized Randall-Sundrum two branes model
• Dynamical system approach to FRW models in higher-order gravity theories
• Beyond the Low Energy Approximation in Braneworld Cosmology
• Gauss-Bonnet braneworld redux: A novel scenario for the bouncing universe
• Scaling solution, radion stabilization, and initial condition for brane-world cosmology
• Radion stabilization with(out) Gauss-Bonnet interactions and inflation
• Linearized Israel Matching Conditions for Cosmological Perturbations in a Moving Brane Background
• Second order perturbations in the radius stabilized Randall-Sundrum two branes model II -- Effect of relaxing strong coupling approximation --
• High-Energy theory for close Randall Sundrum branes