Conformal transformation in the scalar-tensor theory applied to the accelerating universe

TL;DR

This paper investigates the physical equivalence of Jordan and Einstein conformal frames in scalar-tensor theories, especially in the context of the accelerating universe, and discusses conditions under which each frame is physically acceptable.

Contribution

It provides a detailed analysis of conformal frame equivalence in scalar-tensor cosmology, supporting partial equivalence and clarifying the physical interpretation of each frame.

Findings

Partial support for conformal frame equivalence.

Jordan frame suitable for unification theories.

Einstein frame acceptable under specific conditions.

Abstract

The scalar-tensor theory is plagued by nagging questions if different conformal frames, in particular the Jordan and Einstein conformal frames, are equivalent to each other. As a closely related question, there are opposing views on which of the two conformal frames is physically acceptable. Reinforcing our previous claims, we offer replies based on a cosmological model of the scalar-tensor theory, believed to be a promising theory for understanding the accelerating universe, as well as today's version of the cosmological constant problem. Exploiting the advantage that this model admits analytical asymptotic solutions, our argument does not depend on whether the underlying theory is invariant under conformal transformations. Our argument provides partial support for the claimed "equivalence," but we also present examples that require more careful analyses exploiting field equations. We also point out that the Jordan conformal frame is suitable for an interpretation in terms of unification theories in physics, for example, string theory and the Kaluza-Klein approach, while the Einstein conformal frame may be acceptable as a physical conformal frame under two conditions: (i) the simplest constant $\Lambda$ term in the Lagrangian in the Jordan conformal frame; (ii) the revised form of the conventional Brans-Dicke model based on the validity of weak equivalence principle.