The -observable- universe certainly appears to be expanding... but the question of infinity is a whole separate issue because it includes that which may not necessarily be observable.
You might be interested in reading about Einstein's "cosmological constant." Einstein was not satisfied with the notion that the universe should have a finite beginning and end (as his theory of general relativity suggested).
Basically, according to his earlier theories, the universe would inevitably collapse upon itself. He would not accept this outcome.
The "cosmological constant" was a way of avoiding this problem.
For Einstein, the C.C. was just a shot in the dark. He had no evidence supporting this strange modification to his theory of relativity... yet he reluctantly proposed it anyways. I find it very interesting that a man such as Einstein would place so much faith in an intuitive "gut instinct" that he would be willing to take such an arguably unscientific risk on an idea such as the C.C.
Then again, Einstein was more than a great scientist, he was a genius. He used both logic AND intuition in his pursuit of truth. This is a man who is famously quoted as saying: "God does not throw dice."
Sadly, he did not live long enough to learn that he actually may have been right all along about his Cosmological Constant. Recent discoveries pointing to the existence of 'dark matter' (and other "undetectable" particles) may actually be consistent with Einstein's C.C. modification, and have sparked renewed interest in his theories.
Perhaps the good people at CERN will be able to answer these questions for us sometime next year, assuming their fancy new supercollider does not destroy the fabric of spacetime...