Covariant generalization of cosmological perturbation theory

Abstract

We present an approach to cosmological perturbations based on a covariant perturbative expansion between two worldlines in the real inhomogeneous universe. As an application, at an arbitrary order we define an exact scalar quantity which describes the inhomogeneities in the number of e-folds on uniform density hypersurfaces and which is conserved on all scales for a barotropic ideal fluid. We derive a compact form for its conservation equation at all orders and assign it a simple physical interpretation. To make a comparison with the standard perturbation theory, we develop a method to construct gauge-invariant quantities in a coordinate system at arbitrary order, which we apply to derive the form of the n-th order perturbation in the number of e-folds on uniform density hypersurfaces and its exact evolution equation. On large scales, this provides the gauge-invariant expression for the curvature perturbation on uniform density hypersurfaces and its evolution equation at any order.

arXiv commentMinor changes to match the version published in PRD. RevTex, 22 pages, 1 figure

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• Multifield Cosmological Perturbations at Third Order and the Ekpyrotic Trispectrum
• de Sitter limit of inflation and nonlinear perturbation theory
• Cosmological Backreaction from Perturbations
• Conserved cosmological perturbation in Galileon models
• A geometrical approach to nonlinear perturbations in relativistic cosmology
• Gauge invariant Boltzmann equation and the fluid limit
• Second order Boltzmann equation : gauge dependence and gauge invariance
• Vector and tensor contributions to the curvature perturbation at second order
• Practical tools for third order cosmological perturbations
• Comparing different formulations of non-linear cosmological perturbation theory
• Fully non-linear equivalence of delta N and covariant formalisms
• A general proof of the equivalence between the δN and covariant formalisms
• Non-linear effects in early Universe cosmology