What should they use?
What SHOULD they use? The one thing which propogates instantaneously to within our ability to measure it is gravity and the closest thing to a decent explanation of what gravity is, is Ralph Sansbury’s description of gravity and sub-electron particles. The computed necessary speed of a sub-electron particle would get you to one of the near galaxies in a couple of seconds. Anything which anybody with the brains and talent to communicate across cosmic distances would actually use would likely have to involve those kinds of particles.