1+3 covariant dynamics of scalar perturbations in braneworlds

Bernard Leong, Peter Dunsby, Anthony Challinor, and Anthony Lasenby
Phys. Rev. D 65, 104012 – Published 29 April 2002
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Abstract

We discuss the dynamics of linear, scalar perturbations in an almost Friedmann-Robertson-Walker braneworld cosmology of Randall-Sundrum type II using the 1+3 covariant approach. We derive a complete set of frame-independent equations for the total matter variables, and a partial set of equations for the nonlocal variables which arise from the projection of the Weyl tensor in the bulk. The latter equations are incomplete since there is no propagation equation for the nonlocal anisotropic stress. We supplement the equations for the total matter variables with equations for the independent constituents in a cold dark matter cosmology, and provide solutions in the high and low-energy radiation-dominated phase under the assumption that the nonlocal anisotropic stress vanishes. These solutions reveal the existence of new modes arising from the two additional nonlocal degrees of freedom. Our solutions should prove useful in setting up initial conditions for numerical codes aimed at exploring the effect of braneworld corrections on the cosmic microwave background (CMB) power spectrum. As a first step in this direction, we derive the covariant form of the line of sight solution for the CMB temperature anisotropies in braneworld cosmologies, and discuss possible mechanisms by which braneworld effects may remain in the low-energy universe.

  • Received 12 November 2001

DOI:https://doi.org/10.1103/PhysRevD.65.104012

©2002 American Physical Society

Authors & Affiliations

Bernard Leong1,*, Peter Dunsby2,†, Anthony Challinor1,‡, and Anthony Lasenby1,§

  • 1Astrophysics Group, Cavendish Laboratory, Madingley Road, Cambridge CB3 OHE, United Kingdom
  • 2Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch 7701, South Africa

  • *Electronic address: cwbl2@mrao.cam.ac.uk
  • Electronic address: peter@vishnu.mth.uct.ac.za
  • Electronic address: A.D.Challinor@mrao.cam.ac.uk
  • §Electronic address: A.N.Lasenby@mrao.cam.ac.uk

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Vol. 65, Iss. 10 — 15 May 2002

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