Choosing a conformal frame in scalar-tensor theories of gravity with a cosmological constant

TL;DR

This paper investigates conformal frames in scalar-tensor gravity theories with a cosmological constant, proposing modifications to make the Einstein frame viable and exploring implications for fifth forces and observational bounds.

Contribution

It introduces a scale-invariant scalar-matter coupling to address issues with conformal frames in scalar-tensor theories, linking quantum anomalies to fifth forces.

Findings

Neither Jordan nor Einstein frame suitable for primordial nucleosynthesis analysis

Modified theory with scale-invariant coupling makes Einstein frame acceptable

Predicted fifth force is roughly consistent with observational bounds

Abstract

Cosmological solutions of the Brans-Dicke theory with an added cosmological constant are investigated with an emphasis to select a conformal frame in order to implement the scenario of a decaying cosmological constant, featuring an ever growing scalar field. We focus particularly on Jordan frame, the original frame with the nonminimal coupling, and conformally transformed Einstein frame without it. For the asymptotoic attractor solutions as well as the "hesitation behavior," we find that none of these conformal frames can be accepted as the basis of analyzing primordial nucleosynthesis. As a remedy, we propose to modify the prototype BD theory, by introducing a scale-invariant scalar-matter coupling, thus making Einstein frame acceptable. The invariacne is broken as a quantum anomaly effect due to the non-gravitational interactions, entailing naturally the fifth force, characterized by a finite force-range and WEP violation. A tentative estimate shows that the theoretical prediction is roughly consistent with the observational upper bounds. Further efforts to improve the experimental accuracy is strongly encouraged.