Cosmological density fluctuations and gravity waves: A covariant approach to gauge-invariant nonlinear perturbation theory

Chris Clarkson
Phys. Rev. D 70, 103524 – Published 19 November 2004

Abstract

We present a new approach to gauge-invariant cosmological perturbations at second-order, which is also covariant. We examine two cases, in particular, for a dust Friedman-Lemaître-Robertson-Walker model of any curvature: we investigate gravity waves generated from clustering matter, that is, induced tensor modes from scalar modes; and we discuss the generation of density fluctuations induced by gravity waves-scalar modes from tensor perturbations. We derive a linear system of evolution equations for second-order gauge-invariant variables which characterize fully the induced modes of interest, with a source formed from variables quadratic in first-order quantities; these we transform into fully-fledged second-order gauge-invariant variables. Both the invariantly defined variables and the key evolution equations are considerably simpler than similar gauge-invariant results derived by other methods. By finding analytical solutions, we demonstrate that nonlinear effects can significantly amplify or dampen modes present in standard linearized cosmological perturbation theory, thereby providing an important source of potential error in, and refinement of, the standard model. Moreover, these effects can dominate at late times, and on super-Hubble scales.

  • Figure
  • Received 21 November 2003
  • Publisher error corrected 30 November 2004

DOI:https://doi.org/10.1103/PhysRevD.70.103524

©2004 American Physical Society

Corrections

30 November 2004

Erratum

Authors & Affiliations

Chris Clarkson*

  • Relativity and Cosmology Group, Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch 7701, Cape Town, South Africa;
  • Institute of Cosmology and Gravitation, University of Portsmouth, Portsmouth, PO1 2EG, Britain

  • *Electronic Address: chris.clarkson@port.ac.uk

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Issue

Vol. 70, Iss. 10 — 15 November 2004

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