The colonial fleet does not appear to possess the ability to do faster than light communication, other than by sending a message on a ship making an FTL jump.
The Cylons however, indicate a possible capability of FTL communication.
- When a Humanoid Cylon body is killed, the mind of the Cylon downloads to a ressurection tank which is not in the immediate light cone. For example, Boomer was shot onboard the Galactica, and downloaded to Caprica, many light years disant. (Downloaded)
- The Cylons have repeatedly tracked the fleet from long distances. For example, somehow the Olympic Carrier was able to signal the location of the fleet to the Cylons very rapidly after a jump. (33)
- When D'Anna Biers completes her documentary, she is unable to transmit it, but is able to signal for a Cylon Raider to appear to receive transmission of the video, which is then shown at a distant location. Whatever FTL transmitter she has is apparently limited in bandwidth, the the ones in her mind and the mind of the raider are apparently much higher bandwidth. (Final Cut)
- On several occasions, it is indicated that Cylon Base Ships communicate with one another over very long distances, however it is possible this could be done by sending message probes with FTL jump capability.
In contemporary physics, FTL communication is inconsistent with causality, as is FTL propulsion.