If the acceleration is too big universe will be end in a Big Rip. Eventually galaxies will be ripped apart, atoms will be ripped apart, our whole universe will be ripped apart. This will not happen for at least 50 billion years. But if someone can watch this end from one of the stars he will observe that a wall of darkness is coming towards him. Eventually the wall of darkness will cover the entire universe.

It may also end up in a Big Chill. The galaxies will move so far from each other that they will disappear from view. Eventually their energy sources will burn out. The universe will become cold and dark. These ideas are predicted by Albert Einstein and Edwin Hubble, but unfortunately neither of them lived long enough to see the result. For our solar system, sun will be the first to go. Earth will freeze and all other galaxies and starts will go so far away that they will disappear from the view. The dark universe will continue to expand but there will be no one to see it........

But we know very little about Dark Energy which is responsible for the Big Rip or Big Chill. We don't know the physics of Dark Energy and we don't know how it works. If we knew that, we could refine our theory and may found different fate for our universe.