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Fifth forces and frame invariance

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.