Integro-differential equation for brane-world cosmological perturbations
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.
Cite
@article{arxiv.hep-th/0104185,
title = {Integro-differential equation for brane-world cosmological perturbations},
author = {Shinji Mukohyama},
journal= {arXiv preprint arXiv:hep-th/0104185},
year = {2014}
}
Comments
Latex, 13 pages; geometrical interpretation of eq.(36) added, typos corrected, references added; typos corrected again; version to appear in Physical Review D