  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.
