Fifth forces and frame invariance

TL;DR

This paper applies a covariant formalism to scalar-tensor theories to achieve frame-invariant calculations of fifth forces, demonstrating that the suppression of these forces in scale-invariant models holds across all frames, not just specific ones.

Contribution

It extends previous results by using a geometric approach to show fifth force suppression is frame-independent in scalar-tensor theories.

Findings

Fifth force calculations can be made frame-invariant using Vilkovisky-DeWitt formalism.

Suppression of fifth forces in scale-invariant Higgs-dilaton gravity is valid across all frames.

The Jordan and Einstein frames are part of a continuum of frames in a unified field space.

Abstract

I discuss how one can apply the covariant formalism developed by Vilkovisky and DeWitt to obtain frame invariant fifth force calculations for scalar-tensor theories. Fifth forces are severely constrained by astrophysical measurements. It was shown previously that for scale-invariant Higgs-dilaton gravity, in a particular choice of Jordan frame, the dilaton fifth force is dramatically suppressed, evading the observational constraints. Using a geometric approach I extend this result to all frames, and show that the usual dichotomy of "Jordan frame" versus "Einstein frame" is better understood as a continuum of frames: submanifold slices of a more general field space.