Applicability of standard unitarity and causality bounds to gravitational scattering

Determine whether standard unitarity and causality constraints on scattering amplitudes, such as partial-wave unitarity bounds used in non-gravitational quantum field theories, apply straightforwardly to gravitational theories, and clarify how these constraints should be formulated when asymptotic states are ill-defined in curved spacetimes.

Background

The paper discusses partial-wave amplitudes for scalar scattering mediated by gravity and notes that, in non-gravitational quantum field theories, amplitudes must satisfy properties including unitarity and causality. However, the authors caution that even defining asymptotic states in curved spacetime can be challenging or impossible depending on the asymptotic structure, making the straightforward application of standard bounds uncertain in gravitational contexts.

For the purposes of the present calculation, the authors assume standard notions like unitarity and causality hold in flat backgrounds, but they explicitly flag the broader question of whether and how these constraints apply in quantum gravity as unresolved.

References

A priori, it is not clear that all of them also have to apply to gravitational theories in a straightforward way. In particular, even the very definition of asymptotic states in a curved spacetime is challenging if not impossible, depending on the specific asymptotic structure of spacetime under investigation.

— Asymptotically (un)safe scattering amplitudes from scratch: a deep dive into the IR jungle  (2602.21285 - Knorr, 24 Feb 2026) in Section 2, Scalar scattering amplitudes

Whether this persists in $4d$ remains to be seen.

— Bounds on scattering amplitudes of non-identical scalar particles in 4d  (2609.09282 - Ferretti et al., 8 Sep 2026) in Section "Discussion," paragraph "Full system"

A complete analysis of perturbative unitarity is beyond the scope of the present work. Nevertheless, it is an important consistency condition because the relevant parameter regions involve large non-minimal couplings. As is known from Higgs inflation, the perturbative cutoff can depend on the gravitational formulation, the background field configuration, and even the scalar self-coupling through higher-point scattering amplitudes. In MAG, the factor G modifies the scalar kinetic structure, so the cutoff may also depend on the non-minimal couplings and on the background field configuration. We leave a dedicated analysis of this issue for future work.

— Axionic Wormholes in Metric-Affine Gravity  (2609.11010 - Takeshita et al., 10 Sep 2026) in Section 5, Conclusions and Discussion