A general proof of the conservation of the curvature perturbation

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  • 9 November 2004
Abstract
Without invoking a perturbative expansion, we define the cosmological curvature perturbation, and consider its behaviour after smoothing on a comoving scale much bigger than the horizon. We, however, do invoke an expansion in spatial gradients, the so-called gradient expansion. The only essential assumption is that the spatial metric is conformally flat to a sufficiently good approximation. More precisely, a non-conformally flat component is of second order in spatial gradients at most. The results obtained are straight-forward generalisations of those already proven in linear perturbation theory and (in part) in second-order perturbation theory. The equations are simple, resembling closely the first-order equations.

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