Galaxies are moving away from us proportional to the distance between us and them , but nothing can travel faster than light, so even the farmost galaxies should be travelling away from us along with the space time with a speed less than that of light. In that case is our universe finite?
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Galaxies are not moving away from us, it is the space between us and the galaxies (and everything, in general) that is continually expanding. This is allowed to happen faster than the speed of light, because no object actually crosses the light speed barrier in the process. So consequentially, the universe has no size constraint like the one you've stated.
Hritik Narayan
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If you mean by "our universe" the matter in spacetime we are able to reach and observe then you are right. The universe will become more and more finite for us unless someone will invent a "warp drive" or "wormhole" (currently the probability for it is very low).
According to research you have ca. 100bn years time before all others galaxies will be gone beyond the cosmic light horizon. So at this time you are restricted to do your travel and oberservations within Milkdromeda.
https://en.wikipedia.org/wiki/Timeline_of_the_far_future http://arxiv.org/abs/1102.0007v2
But that does not mean that the entire universe is finite. (See comment on top)
Randy Welt
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