Earlier quoted context omitted.
The paradox says that an universe infinite in space and time would have to be bright in all directions. By infinite in time, I mean that the universe has been around infinitely long, i.e. it has no beginning. The finite speed of light wouldn't matter here since the light would have had an infinite amount of time to reach you.
Huh? We definitely know that that doesn't describe the universe. If two points are so far apart that the expansion of space inflates the distance between them faster than light can cross it, then no light can ever reach from one to the other, even if it travels for an infinitely long time.
Actually, it can. The issue is quite subtle. What you are saying is true only if the Hubble parameter is constant, it is not. (Hubble constant is such a misnomer! It's only constant across space but not time).
You may want to re-read paragraph 3.3 of the Lineweaver paper (http://arxiv.org/pdf/astro-ph/0310808v2.pdf)
Quotes :
> Photons near the Hubble sphere that are receding slowly are overtaken by the more rapidly receding Hubble sphere.
> The most distant objects that we can see now were outside the Hubble sphere when their comoving coordinates intersected our past light cone. Thus, they were receding superluminally when they emitted the photons we see now.