paper

Integro-differential equation for brane-world cosmological perturbations

arXiv:hep-th/0104185 · doi:10.1103/PhysRevD.64.064006 10.1103/PhysRevD.66.049902

Abstract

Cosmological perturbations in the brane-world cosmology with a positive tension brane in the AdS background bulk geometry is analyzed by using the doubly gauge-invariant formalism. We derive four independent equations for scalar perturbations in the plane symmetric (K=0) background. Three of these equations are differential equations written in terms of gauge invariant variables on the brane only, and another of them is an integro-differential equation whose kernel is constructed formally from the Z_2-symmetric retarded Green's function of the bulk gravitational waves. We compare these four equations with the corresponding equations in the standard cosmology. As a by-product, we also obtain a set of equations which may be useful in numerical calculations.

Latex, 13 pages; geometrical interpretation of eq.(36) added, typos corrected, references added; typos corrected again; version to appear in Physical Review D

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