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

Abstract

Recently, the equivalence between the δN and covariant formalisms has been shown (Suyama et al. 2012), but they essentially assumed Einstein gravity in their proof. 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 δN 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 δN and covariant formalisms without specifying the slicing condition and the associated slicing coincidence, in other words, regardless of the gravity theory.

7 pages,a reference added, to be published in EPL

References in corpus (17)

• Imperfect Dark Energy from Kinetic Gravity Braiding
• G-inflation: inflation driven by the Galileon field
• Non-gaussianity from the second-order cosmological perturbation
• Primordial non-Gaussianity from the DBI Galileons
• Observational tests of inflation with a field derivative coupling to gravity
• Primordial non-Gaussianities in general modified gravitational models of inflation
• Primordial Non-Gaussianity in Multi-Scalar Slow-Roll Inflation
• Primordial non-Gaussianity from G-inflation
• Primordial fluctuations and non-Gaussianities from multifield DBI Galileon inflation
• Gradient expansion approach to nonlinear superhorizon perturbations
• Conservation of the nonlinear curvature perturbation in generic single-field inflation
• Non-Gaussianity of superhorizon curvature perturbations beyond $\delta$ N formalism
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• Covariant generalization of cosmological perturbation theory
• δN versus covariant perturbative approach to non-Gaussianity outside the horizon in multifield inflation
• Nonlinear superhorizon perturbations of non-canonical scalar field
• Fully non-linear equivalence of delta N and covariant formalisms

Cited by in corpus (6)

• δN Formalism in Anisotropic Inflation and Large Anisotropic Bispectrum and Trispectrum
• Primordial Anisotropies in Gauged Hybrid Inflation
• \bf $\delta M$ Formalism: A New Approach to Cosmological Perturbation Theory in Anisotropic Inflation
• Consistency relation and inflaton field redefinition in the delta N formalism
• Two-field inflation with non-minimal coupling
• $\Delta N$ Formalism and Conserved Currents in Cosmology