Anomalous Dispersion in Gravity Theories

TL;DR

This paper investigates how anomalous dispersion of wave pulses occurs in flat spacetimes with even spatial dimensions and shows that in certain gravity theories and backgrounds, dispersion can be eliminated, restoring classical wave propagation.

Contribution

It demonstrates that in even-dimensional flat spacetimes, anomalous dispersion can be avoided in de Sitter backgrounds with massive gravity tuned to the cosmological constant.

Findings

Anomalous dispersion occurs in flat even-dimensional spacetimes.

De Sitter backgrounds can eliminate anomalous dispersion.

Tuned massive gravity restores Huygens' principle.

Abstract

A wave pulse (be it a gravitational wave or a light wave) undergoes anomalous dispersion in a vacuum in flat spacetimes with an even number of spatial dimensions even if all the frequencies move at the same speed. Such an anomalous dispersion does not occur in spacetimes with an odd number of spatial dimensions. We study various gravity theories and show that dispersion-free propagation is possible in even number of spatial dimensions if the background is not the Minkowski but the de Sitter spacetime and the gravity theory is massive gravity with a tuned mass in terms of the cosmological constant. Mass and the cosmological constant conspire to get rid of the anomalous dispersion and restore Huygens' principle.