Hi Jim
Best place for a mathematical description of cosmic distances is Prof. Ned Wright's tutorial here...
http://www.astro.ucla.edu/~wright/cosmolog.htm
...from the main page you can navigate to all sorts of handy tools, like the cosmic calculator...
http://www.astro.ucla.edu/~wright/CosmoCalc.html
...for example because the Universe has expanded since the Big Bang, the most distant galaxy recently discovered at red-shift z = 10 is now 31.5 billion light years away even though light from it has taken a mere 13.2 billion years to get here. Nothing within space-time has travelled faster-than-light, but space-time itself has expanded faster-than-light, which is fine in general relativity.
That's incidently how the Alcubierre warp-drive works - by expanding space-time in front of a ship and contracting it behind the ship.
Space/Science » in reply to Hubble Ultra Deep Field and age of the Universe
Space-time expansion...
