A general proof of the equivalence between the δN and covariant formalisms

Details A general proof of the equivalence between the δN and covariant formalisms A general proof of the equivalence between the δN and covariant formalisms

2012-02-07

arxiv.org/abs/1202.1516v1

Astronomy and Astrophysics

Astrophysics

Cosmology and Extragalactic Astrophysics

6 pages

Scientific paper

Recently, the equivalence between the \delta N and covariant formalisms has been shown, but they assumed Einstein gravity in their proof [arXiv:1201.3163]. They showed that the evolution equation of the curvature covector in the covariant formalism on uniform energy density slicings coincides with that of the curvature perturbation in the \delta N formalism assuming the coincidence of uniform energy and uniform expansion (Hubble) slicings, which is the case on superhorizon scales in Einstein gravity. In this short note, we explicitly show the equivalence between the \delta N and covariant formalisms without specifying the slicing condition and the associated slicing coincidence, in other words, regardless of the gravity theory.

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