Frame independent cosmological perturbations

Abstract

We compute the third order gauge invariant actionfor scalar-graviton interactions in the Jordan frame.We demonstrate that the gauge invariant actionfor scalar and tensor perturbations on one physical hypersurfaceonly differs from that on another physical hypersurfacevia terms proportional to the equation of motionand boundary terms, such that the evolution ofnon-Gaussianity may be called unique.Moreover, we demonstrate that thegauge invariant curvature perturbation and gravitonon uniform field hypersurfaces in the Jordan frameare equal to their counterparts in the Einstein frame.These frame independent perturbations are thereforeparticularly useful in relating results in differentframes at the perturbative level. On the other hand,the field perturbation and gravitonon uniform curvature hypersurfaces in the Jordanand Einstein frame are non-linearly related, as aretheir corresponding actions and n-point functions.