Possibility of Landau damping of gravitational waves

There is considerable uncertainty in the literature concerning whether or not transverse traceless gravitational waves can Landau damp. Physically, the issue is whether particles of nonzero mass can comove with surfaces of constant wave phase, and therefore, loosely, whether gravitational waves can have phase speeds less than that of light. We approach the question of Landau damping in various ways. We consider first the propagation of small-amplitude gravitational waves in an ideal fluid-filled Robertson-Walker universe of zero spatial curvature. We argue that the principle of equivalence requires those modes to be lightlike. We show that a freely moving particle interacting only with the collective fields cannot comove with such waves if it has nonzero mass. The equation for gravitational waves in collisionless kinetic gases differs from that for fluid media only by terms so small that deviations from lightlike propagation are unmeasurable. Thus, we conclude that Landau damping of small-amplitude, transverse traceless gravitational waves is not possible