Conformal-Frame (In)dependence of Cosmological Observations in Scalar-Tensor Theory

TL;DR

This paper investigates the frame-(in)dependence of cosmological observables in scalar-tensor gravity, showing that key observables are frame-independent while certain perturbations depend on the frame under specific conditions.

Contribution

It clarifies the conditions under which cosmological observables and curvature perturbations are invariant or dependent on the choice of frame in scalar-tensor theories.

Findings

Cosmological observables like redshift and luminosity distance are frame-independent.

Curvature perturbations are conformal invariant if adiabatic and entropy perturbation vanishes.

The paper discusses the relations among different curvature perturbation definitions in both frames.

Abstract

We provide the correspondence between the variables in the Jordan frame and those in the Einstein frame in scalar-tensor gravity and consider the frame-(in)dependence of the cosmological observables. In particular, we show that the cosmological observables/relations (redshift, luminosity distance, temperature anisotropies) are frame-independent. We also study the frame-dependence of curvature perturbations and find that the curvature perturbations are conformal invariant if the perturbation is adiabatic and the entropy perturbation between matter and the Brans-Dicke scalar is vanishing. The relation among various definitions of curvature perturbations in the both frames is also discussed, and the condition for the equivalence is clarified.