Disformal transformation of cosmological perturbations

TL;DR

This paper studies how cosmological perturbations transform under disformal transformations in scalar-tensor theories, revealing invariance properties and evolution equations across different frames.

Contribution

It extends the understanding of gauge-invariant perturbations by analyzing disformal transformations, showing invariance of certain curvature perturbations and deriving frame-independent evolution equations.

Findings

Curvature perturbation in comoving gauge is disformally and conformally invariant.

In matter sector, curvature perturbation evolution equations are derived and are frame-independent.

Conservation of curvature perturbation depends on the gauge and frame, with specific conditions identified.

Abstract

We investigate the gauge-invariant cosmological perturbations in the gravity and matter frames in the general scalar-tensor theory where two frames are related by the disformal transformation. The gravity and matter frames are the extensions of the Einstein and Jordan frames in the scalar-tensor theory where two frames are related by the conformal transformation, respectively. First, it is shown that the curvature perturbation in the comoving gauge to the scalar field is disformally invariant as well as conformally invariant, which gives the predictions from the cosmological model where the scalar field is responsible both for inflation and cosmological perturbations. Second, in case that the disformally coupled matter sector also contributes to curvature perturbations, we derive the evolution equations of the curvature perturbation in the uniform matter energy density gauge from the energy (non)conservation in the matter sector, which are independent of the choice of the gravity sector. While in the matter frame the curvature perturbation in the uniform matter energy density gauge is conserved on superhorizon scales for the vanishing nonadiabatic pressure, in the gravity frame it is not conserved even if the nonadiabatic pressure vanishes. The formula relating two frames gives the amplitude of the curvature perturbation in the matter frame, once it is evaluated in the gravity frame.