Frame independent cosmological perturbations

TL;DR

This paper derives a gauge invariant third order action for scalar-graviton interactions in the Jordan frame, showing the frame independence of certain perturbations and their implications for cosmological non-Gaussianity.

Contribution

It provides a frame-independent formulation of cosmological perturbations at third order, clarifying their relation in Jordan and Einstein frames.

Findings

Gauge invariant actions differ only by boundary terms and equations of motion.

Curvature perturbation and graviton are frame-independent on uniform field hypersurfaces.

Field perturbation and graviton are non-linearly related across frames.

Abstract

We compute the third order gauge invariant action for scalar-graviton interactions in the Jordan frame. We demonstrate that the gauge invariant action for scalar and tensor perturbations on one physical hypersurface only differs from that on another physical hypersurface via terms proportional to the equation of motion and boundary terms, such that the evolution of non-Gaussianity may be called unique. Moreover, we demonstrate that the gauge invariant curvature perturbation and graviton on uniform field hypersurfaces in the Jordan frame are equal to their counterparts in the Einstein frame. These frame independent perturbations are therefore particularly useful in relating results in different frames at the perturbative level. On the other hand, the field perturbation and graviton on uniform curvature hypersurfaces in the Jordan and Einstein frame are non-linearly related, as are their corresponding actions and $n$-point functions.