The effect of matter discreteness on gravitational wave propagation in post-geometrical optics

Abstract The gravitational wave equation of motion includes direct coupling to the Riemann tensor. The curvature terms are usually neglected, but they can be large at the location of matter particles and impact the angular diameter distance. We apply the recently introduced post-geometrical optics approximation that includes curvature to gravitational wave propagation. Assuming that particles are localised within their Compton wavelength, the curvature due to electrons leads to a large effect on the angular diameter distance, but caustic formation invalidates the post-geometrical optics approximation. We conclude that the interesting regime of validity of the approximation is limited, as it ceases to apply when the curvature effects become large. Other methods are needed to evaluate the effect of curvature spikes, and the localisation of particles due to decoherence also needs further work.