Brane Gravity at Low Energy

Abstract

Four dimensional gravity in the low energy limit of a higher dimensional theory has been expected to be a (generalized) Brans-Dicke theory. A subtle point in brane world scenarios is that the system of four dimensional effective gravitational equations is not closed due to bulk gravitational waves and bulk scalars. Nonetheless, weak gravity on the brane can be analyzed completely. We revisit the theory of weak brane gravity using gauge-invariant gravitational and scalar perturbations around a background warped geometry with a bulk scalar between two flat branes. We obtain a simple condition for the radion stabilization in terms of the scalar field potentials. We show that for general potentials of the scalar field which provides radion stabilization and a general conformal transformation to a frame in which matter on the branes are minimally coupled to the metric, 4-dimensional Einstein gravity, not BD gravity, is restored at low energies on either brane. In contrast, in RS brane world scenario without a bulk scalar, low energy gravity is BD one. We conjecture that in general brane world scenarios with more than one scalar field, one will again encounter the situation that low energy gravity is not described by the Einstein theory. Equipped with the weak gravity results, we discuss the properties of 4d brane gravitational equations, in particular, the value and sign of 4d Newton's gravitational coupling.

Latex, 22 pages, 1 figure; version accepted for publication in Phys.Rev.D

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• Brane World Sum Rules
• BPS Branes in Cosmology
• Strongly Coupled Grand Unification in Higher Dimensions
• Integro-differential equation for brane-world cosmological perturbations
• Second order perturbations in the radius stabilized Randall-Sundrum two branes model
• Doubly covariant action principle of singular hypersurfaces in general relativity and scalar-tensor theories

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• Six-dimensional localized black holes: numerical solutions
• Cosmology with Radion and Bulk Scalar Field in Two Branes Model
• Braneworld dynamics with the BraneCode
• Nonlocal braneworld action: an alternative to Kaluza-Klein description
• Warm intermediate inflation in the Randall-Sundrum II model in the light of Planck 2015 and BICEP2 results: A general dissipative coefficient
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• Gravity in the dynamical approach to the cosmological constant
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• Kaluza-Klein two-brane-worlds cosmology at low energy
• Second order perturbations in the radius stabilized Randall-Sundrum two branes model II -- Effect of relaxing strong coupling approximation --
• The Dynamics of Brane-World Cosmological Models
• Five-dimensional warped product space-time with time-dependent warping and a scalar field in the bulk