Nietzsche's doctrine of eternal recurrence was partially influenced by Eastern philosophy and may have a basis in science.
Controversial theoretical physicist Peter Lynds suggested a model of eternal recurrence in a 2006 paper. Lynds hypothesizes that if the universe undergoes a big crunch, the arrow of time may reverse. Others have approached the question of eternal recurrence from a physics perspective in different ways, including a hypothesis based on the transactional interpretation of quantum mechanics. Other cosmologists such as Massachusetts Institute of Technology professor Max Tegmark consider the possibility that the known universe is just one of many in a multiverse, presenting the argument that existences identical to our own recur infinitely over infinite space.
http://en.wikipedia.org/wiki/Eternal_re ... _cosmology
On a finite universe with no beginning or end
If you were destined to live your life an infinite number of times, how would you choose to live in the here and now? Eternal recurrence in this world might be a better motivator for right living than a belief in an afterlife such as a heaven to escape this world.