Is there a theory that the beginning and the ending of the universe are directly connected to each other? And that time doesn't so much start over and return to the starting point on a circle, so to speak?
I once heard of the hypothesis that once the last proton decays, the universe will once more be completely uniform in every way. With nothing to distinguish any part of the universe from any other part, space becomes meaningless and the universe has once more entered a state of nothingness much like how it was "before" the Big Bang.
So, in a sense, the heat death is not so different from the big bounce.
Unfortunately I did not bother to bookmark what I had read, and can no longer find a name or anything referring to it on the internet.
Roger Penrose believes in a model he calls Conformal Cyclic Cosmology. He doesn't believe in Cosmic Inflation, and instead proposes that the accelerating expansion of our present universe forms the inflationary period of the next universe. He gets around the second law of thermodynamics by saying that the difference between the two universes is a redefinition of entropy. The mapping between the two different definitions of entropy makes our maximal entropy state look like a minimal entropy state in the new universe.
