Conformal invariance of curvature perturbation

TL;DR

This paper proves that in single-component cosmological models, all perturbation variables in the comoving gauge are conformally invariant at all orders, and identifies a special slicing where all perturbations are conformally invariant, applying this to the delta N formalism.

Contribution

It demonstrates conformal invariance of perturbations in single-component models and introduces a special slicing where this invariance holds at all perturbation orders.

Findings

Perturbation variables in the comoving gauge are conformally invariant at all orders.

A special time slicing, the uniform-conformal transformation slicing, maintains conformal invariance.

The delta N formalism is shown to be conformally invariant.

Abstract

We show that in the single component situation all perturbation variables in the comoving gauge are conformally invariant to all perturbation orders. Generally we identify a special time slicing, the uniform-conformal transformation slicing, where all perturbations are again conformally invariant to all perturbation orders. We apply this result to the delta N formalism, and show its conformal invariance.