Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2006-11-03
Phys.Rev.D75:023515,2007
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
Minor changes to match the version published in PRD. RevTex, 22 pages, 1 figure
Scientific paper
10.1103/PhysRevD.75.023515
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.
Enqvist Kari
Hogdahl Janne
Nurmi Sami
Vernizzi Filippo
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