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Conserved non-linear quantities in cosmology

David Langlois·Filippo Vernizzi
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Abstract

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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David Langlois, Filippo Vernizzi. 2006-02-24. Conserved non-linear quantities in cosmology. https://doi.org/10.1103/physrevd.72.103501

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