de Broglie matter waves are phase (pilot) waves and their velocities (w's) are given by
where c is the speed of light and v is the particle velocity. The superluminal phase velocity is not a contradiction of special relativity since the phase waves do not carry signal or energy. But the group velocity is equivalent to the measured velocity of the particle, which is always less than c.
This seems to imply that for a particle that is absolutely at rest, its phase velocity is infinity. So, if the universe has zero linear momentum it's at rest for all practical purposes and hence its phase velocity is infinity but its wave function is also zero.