Conserved non-linear quantities in cosmology

Details Conserved non-linear quantities in cosmology Conserved non-linear quantities in cosmology

2005-09-05

arxiv.org/abs/astro-ph/0509078v3

Phys.Rev.D72:103501,2005

Astronomy and Astrophysics

Astrophysics

22 pages. v2: published version; v3: corrected Eq. (24)

Scientific paper

10.1103/PhysRevD.72.103501

We give a detailed and improved presentation of our recently proposed formalism for non-linear perturbations in cosmology, based on a covariant and fully non-perturbative approach. We work, in particular, with a covector combining the gradients of the energy density and of the local number of e-folds to obtain a non-linear generalization of the familiar linear uniform density perturbation. We show that this covector obeys a remarkably simple conservation equation which is exact, fully non-linear and valid at all scales. We relate explicitly our approach to the coordinate-based formalisms for linear perturbations and for second-order perturbations. We also consider other quantities, which are conserved on sufficiently large scales for adiabatic perturbations, and discuss the issue of gauge invariance.

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