The conformal frame freedom in theories of gravitation

TL;DR

The paper argues that classical predictions in scalar-tensor gravitation are invariant under conformal-frame transformations, reinforcing physical equivalence across frames (e.g., Jordan vs Einstein) when conventions are not fixed. It surveys classical and quantum considerations of frame freedom, emphasizing that observable quantities are frame-invariant and that the EFT equivalence theorem ensures tree-level results are frame-independent. It then analyzes the Palatini $1/R$ gravity proposal, detailing its reduction to GR with a modified matter sector and exposing objections about physical frames, while demonstrating that experimental constraints at low energies and strong coupling regimes challenge the viability of this model for cosmic acceleration. Overall, the work clarifies conformal-frame invariance in classical gravity and casts doubt on the viability of the Palatini $1/R$ approach as a model of cosmic acceleration, while preserving the importance of careful frame analysis in gravitational theories.

Abstract

It has frequently been claimed in the literature that the classical physical predictions of scalar tensor theories of gravity depend on the conformal frame in which the theory is formulated. We argue that this claim is false, and that all classical physical predictions are conformal-frame invariants. We also respond to criticisms by Vollick [gr-qc/0312041], in which this issue arises, of our recent analysis of the Palatini form of 1/R gravity.