It stands to reason. Afterall, everything else we observe in nature is cyclical, including life. Why wouldn't we expect the universe as a whole to be the same?
I like the multiverse theory that there is a mass of universes like foam, wherein new universes bubble up, some lasting short periods of time, and others lasting longer. When one bubble universe "dies", another is formed as a result.
Might as well post this video, it fits with the theme: