"Milky Way" galaxy will "collide" with the neighboring Andromeda galaxy in about 3-4 billion years. However, galaxies don't collide with each other in the way that objects like cars do. The distances between stars in a typical galaxy are so great that even when the collision is taking place the stars are still an average of a light year or so apart. The main changes are brought about by the gravitational effects that the two giant systems have on each other over the course of many millions of years of the interaction.
As to the "contraction" of the Universe that you speak of, it is seems less and less likely. If you want to make your head hurt think of this. Our Universe is probably a singularity. It will go on expanding and that expansion is actually accelerating until it suffers "heat death" in a trillion years. If you could come forward to that era in a time machine you would see little or no light in the sky. The stars would be too far away or burned out and the Earth would be long gone being absorbed by the Sun as it expands due to its hydrogen fuel being used up before it, too, burned out and became dark. It was comforting to think that our Universe may have the same kind of birth and death cycles as we see on Earth but it isn't so.
= new reply since forum marked as read
