Well, what the website described, as far as I can see, is nonsense. Even if there was some reason for the universe to repeatedly stop growing for a while, it would not be infinitely old. The whole reason we believe there was a Big Bang is that we observe that all galaxies are flying away from us; then we just extrapolate backwards in time.
What you described is actually an extremely well known cosmological theory. If there is a high amount of mass in the universe, this would be true. However, by current estimates, there is not enough, by a factor of around 100; the universe will continue expanding forever, and fizzle out.
Personally I believe that there are many universes though.
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