If the universe is infinite now it has always been infinite. This is the opinion of many astronomers today as can be concluded from the following series of interviews, but the opinions differ much more than I had expected.
Many astronomers do not have a clear opinion on this matter. Others have a clear opinion, but very different from the majority. Detailed arguments by two experts on general relativity are also included.
Observations show that the universe is flat, i.e. the curvature is zero within the small uncertainty of measurements.
This implies an infinite universe, though most probably we will never know that for certain. For comparison with the recent interviews, opinions during the past 2300 years since Aristotle about the universe being finite or infinite have been collected from literature, and it appears that the scientists often had quite definite opinions…
… Read more at http://arxiv.org/ftp/arxiv/papers/1408/1408.4795.pdf