Here's a pretty good article that suggests that the universe is infinite:
The Universe as we know it began with the hot Big Bang 3.8 billion years ago. But the question is the universe finite or infinite?
magnifymind.com
"If the universe were finite, we would expect to see a limited number of galaxies beyond a certain distance.
However, surveys of the sky have found an ever-increasing number of galaxies at ever-greater distances, suggesting that there is no edge to the universe.
Another piece of evidence comes from the study of cosmic background radiation.
This radiation is thought to be left over from the Big Bang, and its properties can tell us something about the size and shape of the universe.
The fact that this radiation appears to be uniform in all directions suggests that the universe is infinite. In conclusion, while we cannot say for certain that the universe is infinite, the evidence suggests that it is indeed without end."