Nietzsche came up with the idea of Eternal Return as a basis of moral choice. It is a hypothetical. Act as if whatever you did you would be doing eternally, and repeating it over and over forever. Could you bear that. If not don’t do it. This is the free spirit’s answer to how to make moral choices in the absence of God. But to get it another transcendental has to be projected, i.e. samsara.
So given the other answers to this question, one must ask can you do the same action again, even if you want to. Deleuze attacks that question in Difference and Repetition, and the answer is NO. The summary is Repetition is that which does NOT repeat. In other words we can do ontic repetitions of some act, say in ritual or obsessive compulsive syndrome, but at an ontological level that does not achieve Repetition. So for instance in Vedic society when they sacrificed it was to achieve wholeness, but it was through the dismemberment of something whole, so the wholeness on the ontological level was not achieved by destroying wholeness on the ontic level. The repetition of sacrifice did not regain the primordial wholeness of Parusha, or of the Indo-European Giant which was the source of all things. To repeat is to inscribe minimal difference between copies, yet that is difference, and the difference prevents the copies from being the same as the original as we know from Art, where the original is what has value.
So if we cannot repeat an action because almost all systems in which actions are taken are non-commutative, not to mention non-associative, then how can the universe which we project as a mirror reflection of ourselves repeat the earth, and even if it repeated the earth, how could we repeat evolution, and if we repeated evolution how could we repeat all the historical accidents that led to you and me in the lives of the 80 billion or so humans that ever existed. In other words, each thing in its circumstances is unique. The confluence of identity and difference is uniqueness. It is all the meta-levels of difference and identity at the various meta-levels of Being that assures this. Eternal Return is a Transcendental in time that cannot happen, just as the idea that time is linear does not stand up either, and as Heidegger points out in Being and Time the moments of time are equi-primordial. There are three canonical moments of time (Past, Present, Future). In Old English there is only complete and incomplete where Past and Future collapse together. Prior to the Metaphysical age in the Mythopoietic there was a fourth moment of time which was mythos, the co-now. Eternal Return is an image of the Co-now, i.e. the virtual now that haunts every now.
This question appeals to the co-now, the virtual now, to ask whether it is possible in eternal return to get to the same place again in time. The answer is no. Even if the universe was infinite, there would be infinite difference and the idea that there would be repetition in infinity, assumes that infinity is linear. But we know that at the various Cardinal Alphs it is impossible to know how far apart there are, so the measure is lost in infinity that would allow for the repetition at the limit of infinity to bring us back to precisely the same spot again. The limits are all impossibilities.
So really what Eternal Return teaches us is to enjoy the moment because it will never repeat. As Buddhism says Samsara is empty, and the truth is Nirvana the freedom from samsara. Nietzsche misunderstood Buddhism seeing it as fatalistic. Because of that he fell into the very mistaken idea that Buddhism was trying to solve, and thought that Samsara could give a principle for ordering life and action, which is wrong. Nietzsche was reacting to Schopenhauer’s misinterpretation of Buddhism based on Hinayana texts that were seen to be the origin of Buddhism. It was Hegel that got it right and identified the nothing at the bottom of his dialectical logic with Buddhist emptiness. He said that emptiness/nothing and Being gave the synthesis of Heraclitian Flux, and out of that flux arises a determinate thing, i.e. the existent Dasein, which then Heidegger made the hero of Being and Time. Because it is Dasein that projects spacetime and the categories as Kant said which then gives rise to the world in which Dasein finds itself. If this is true, as western idealism has posited then it is you as a unique being that gives rise to the spacetime that you would want to repeat, and that is blatantly impossible. The repetition assumes that there could be an objective spacetime beyond our projections, which we all believe but that is a nomena, just like the mutiverse out of which the new universe would have to arise.
Since the multiverse is a noumena, then the answer has to be unknown, but probably not, rather than just no, because the multiverse is famously the unknown unknown, because we can never experience it due to the fact that it is beyond our universe, and thus beyond spacetime even in its objective form if there is such a thing which we cannot know. So this question is metaphysical even though it appears to be about something physical like the repetitions of the universe and the earth within the universe and ourselves as evolved animals on the earth given our unique history. This is why Heidegger says that Nietzsche is the last metaphysician and thus the last philosopher in the Metaphysical age.