Wave-optics gravitational wave lensing in modified gravity

TL;DR

This paper explores how gravitational-wave lensing behaves in the wave-optics regime within modified gravity theories, revealing infrared effects that differ from general relativity and can be probed through scattering amplitude interpretations.

Contribution

It introduces a framework for wave-optics gravitational-wave lensing in modified gravity, highlighting infrared dynamics and a new interpretation involving distorted wave basis and scattering amplitudes.

Findings

Infrared dynamics differ from GR due to curvature-induced interactions.

Standard Fresnel approximation breaks down at low frequencies.

Wave-optics lensing can detect propagation-level deviations from GR.

Abstract

We initiate the study of gravitational-wave lensing in the wave-optics regime within modified gravity. We consider a phenomenological setup in which the gravitational-wave amplitude obeys a curvature-coupled propagation equation. This framework reproduces the standard GR behaviour in the geometric-optics regime, while leading to qualitatively different infrared dynamics. In particular, the usual argument implying that the amplification factor approaches unity in the zero-frequency limit no longer applies. This is due to the persistence of curvature-induced interactions in the infrared, which modify the natural propagation basis itself. As a result, the standard Fresnel treatment ceases to be valid at sufficiently low frequency. The correct infrared regime is instead controlled by an interacting static Green function, with a finite-frequency completion provided by a partial-wave formulation. We show that this structure admits an equivalent distorted-wave interpretation, in which the curvature interaction is absorbed into a dressed reference propagation basis, while the residual lensing effect is encoded in finite-frequency phase shifts. We further demonstrate that these phenomena admit a natural interpretation in the language of scattering amplitudes. Wave-optics lensing can therefore probe propagation-level departures from GR that remain entirely invisible in geometric optics.