Eternal Return, also known as Eternal Recurrence is a concept that the Universe has been recurring, and will continue to recur, in a self-similar form an Infinite number of times across Infinite time or space. The concept is found in Indian Philosophy and in Ancient Egypt and was subsequently taken up by the Pythagoreans and Stoics. In addition, the philosophical concept of Eternal Recurrence was addressed by Arthur Schopenhauer. It is a purely physical concept, involving no supernatural Reincarnation, but the return of beings in the same bodies. Time is viewed as being not linear but cyclical.
The basic premise proceeds from the assumption that the probability of a world coming into existence exactly like our own is greater than zero (we know this because our world exists). If Space is Infinite, then Cosmology tells us that our existence will recur an infinite number of times. In 1871, Louis Auguste Blanqui, assuming a Newtonian Cosmology, where time and space are Infinite, claimed to have shown that the Eternal Recurrence was a Mathematical certainty. In the post-Einstein period, there were doubts that time or space was in fact Infinite, but many models existed which provided the notion of spatial or temporal Infinity required by the Eternal Return hypothesis.
“Time is Infinite, but the things in time, the concrete bodies, are Finite. They may indeed disperse into the smallest particles; but these particles, the atoms, have their determinate numbers, and the numbers of the configurations which, all of themselves, are formed out of them is also determinate. Now, however long a time may pass, according to the Eternal Laws governing the combinations of this Eternal play of repetition, all configurations which have previously existed on this Earth must yet meet, attract, repulse, kiss, and corrupt each other again…”