Both are correct, although the first can be further explained a bit. I won't give you a mathematical proof, though; Instead I'll play with characters.
Let's assume, for the sake of gedankenexperiment, that:
- The speed of light is 5 characters/sec;
- our universe is expanding at 1 character per 5 characters per sec.
This is our current universe, and we launch a photon from body A aiming at body E.
(Space generated each second is marked with a
T=0s A----B----C----D----E Bodies
* Photon - 19 chars to E
--#--* 17 chars to E
--#-----#-* 17 chars to E
--#-----#-----#* 18 chars to E
--#-----#-----#-----#* 19 chars to E
I know, the graph isn't too granular, and the space generation isn't evenly distribute. I apologize for that, but it's for the sake of demonstration.
Notice that at
T=2 some space is already generated between A and the photon. But that's irrelevant: E is sitting at the event horizon, and will never be reached by the photon, because the amount of space being generated between photon
* and body
E is equal, or superior, to the speed of light.
Given any positive expansion rate, there will be an event horizon - a point where the accumulated dilation of space is more than the amount of space a particle moving at the speed of light can travel.
A galaxy sitting initially at say, 1000 characters from A at T=0, will be at staggering 1200C at T=1 - that's 40 times our speed of light.
At T=16s, B (that was passed by the original photon at T=1) will be sitting exactly where E was relative to A, and at T=17 will fall out of our event horizon. A new photon emitted from A will never reach it.