Quantum equivalence of conformal frames in scalar–tensor gravity

Determine whether the equivalence of conformal frames in scalar–tensor gravity persists fully at the quantum level, including the effects of quantum corrections and covariant-phase-space boundary terms.

Background

The paper establishes a classical equivalence between Jordan- and Einstein-frame descriptions in Brans–Dicke theory through an invertible conformal field redefinition, provided the transformation is regular. It explicitly limits this conclusion to the classical theory and notes that quantum equivalence is more subtle.

The unresolved issue concerns whether the two conformal-frame formulations define equivalent quantum theories. The paper points to prior work discussing this question but does not resolve it.

References

Our statements are purely classical. At the quantum level the equivalence of conformal frames is a subtler and partly open question, see e.g. [54].

— Asymptotic flatness beyond General Relativity  (2608.14204 - Maibach, 14 Aug 2026) in Section III A, footnote 5, p. 18

A comparison between the results of calculations in the first and second orders of the slow-roll parameters and observing some tiny differences gives some traces of possibility to judge about perfect physical equivalency of these two mathematically and equivalent frames. To be more clarified, it seems that higher order calculations of the inflation observables in this non-minimal unimodular setup signals the possibility of non-equivalency of these two frames on physical ground. This issue is under study and will be reported in future.

— Non-minimal Unimodular Inflation  (2608.20095 - Malekpour et al., 20 Aug 2026) in Section 7, Conclusion

A rigorous proof of the equivalence of local equilibrium between frames is beyond the scope of the present investigation, and we leave this question for future work.

— Non-Minimally Coupled Warm Inflation in the Defining Frame  (2608.20293 - Casado-Turrión et al., 20 Aug 2026) in Section 3.1, discussion following the perturbed Einstein-frame equations; Summary and Conclusions

In contrast, for the action written in the Einstein frame, $\Phi$ (or equivalently $\tilde{\Phi}$) couples to all matter fields. Accounting for all these additional interactions in full generality may be particularly challenging, if not impossible. Moreover, such a computation would have to confront the issue of frame equivalence at the quantum level, which is still an unsolved issue .

— Non-Minimally Coupled Warm Inflation in the Defining Frame  (2608.20293 - Casado-Turrión et al., 20 Aug 2026) in Section 2.1, discussion following Eq. (tilde_dc); Summary and Conclusions