I think we should call this thread "LHC reloaded". xD
It was mentioned that the universe is expanding at an infinite rate. That is not what we currently believe. However, as of now, we're still unsure of the exact value. Observations suggest that the universe is expanding and this is how we came up with the expanding/contracting universe theory.
Latest progress on this matter is reported
here.
As for infinity, it is essentially a creature that no one knows about. We necessitated the need for it because, like Ralath said, there are instances where we have to allow for it, like the set of numbers, for example. If we define a natural number such that there exists another natural number that is 1 more than it, then there has to be an infinite number of natural numbers, simply by using induction.