Can weak-gravity, causality-violation arguments constrain modified gravity?

TL;DR

This paper examines the limitations of causality-based constraints on modified gravity theories, showing they are less restrictive than astrophysical bounds and only valid in weak-gravity regimes, especially for theories like dynamical Chern-Simons gravity.

Contribution

It demonstrates that causality constraints from flat-spacetime amplitudes are limited to weak gravity and are weaker than astrophysical constraints, providing detailed analysis for dynamical Chern-Simons gravity.

Findings

Causality constraints are only valid in the weak-gravity regime.

Time delays for compact objects are suppressed by the mass-to-impact parameter ratio.

Time delays in shockwave solutions are always positive within the regime of validity.

Abstract

We investigate limitations of causality arguments from flat-spacetime amplitudes, based on the eikonal limit of gravitational scattering, to place constraints on modified gravity. We show that causality constraints are only valid in the weak-gravity regime even for transplanckian scattering, and that such constraints are much less stringent than astrophysical ones, obtained for example from gravitational waves emitted in black hole coalescence. Special attention is given to the weakness of causality constraints on dynamical Chern-Simons gravity, but our results apply to other modified gravity theories as well. In the context of that theory, we also discuss how to obtain a time-delay formula from black hole, neutron stars, and shockwave solutions. For scattering with compact objects, we explicitly show that time delays are greatly suppressed by the ratio of the object's mass to the impact parameter, so time advances only occur greatly outside the cut off of the theory. For the shockwave solution, we find that the time delay is always positive within the regime of validity of the solution. We also comment on the impact of graviton nonlinearities for time-delay calculations in the nonlinear, strong gravity regime. We conclude that amplitude-based causality constraints on modified gravity are typically not stringent relative to other experimental and observational bounds.