The (pseudo)issue of the conformal frame revisited

TL;DR

This paper revisits the equivalence of Jordan and Einstein frames in scalar-tensor gravity, clarifying classical and quantum differences, and addressing issues like units, singularities, and the cosmological constant problem.

Contribution

It provides a detailed analysis of the classical and quantum equivalence of conformal frames, resolving paradoxes and clarifying the role of units and singularities.

Findings

Classical frames are physically equivalent.

Quantum inequivalence of frames is demonstrated.

Clarification of the cosmological constant problem in Einstein frame.

Abstract

The issue of the equivalence between Jordan and Einstein conformal frames in scalar-tensor gravity is revisited, with emphasis on implementing running units in the latter. The lack of affine parametrization for timelike worldlines and the cosmological constant problem in the Einstein frame are clarified, and a paradox in the literature about cosmological singularities appearing only in one frame is solved. While, classically, the two conformal frames are physically equivalent, they seem to be inequivalent at the quantum level.