A few decades ago, that was widely believed as the most likely state of the universe. However, it's now known that the big bang is essentially still accelerating and this is blamed on an unknown force called "dark energy". It doesn't have much effect within galaxies, but galaxies themselves are blowing away from each other at ridiculous speeds.
Well it's more that space itself is expanding. It doesn't affect small scales because other forces collapse everything back together fast enough to overcome it. If the increase in dark energy is consistent though, eventually it'll be expanding so fast not even our atoms can hold themselves together.
