The current top contender for developing an overall mathematical model of the entire Universe is “M-theory”, a generalisation of String theory. In M-theory, the Universe has 11 dimensions, but contains many independent sub-Universes, such as our own, with fewer dimensions. It’s not clear whether the big Universe or the sub-Universes are finite or infinite; or whether the number of sub-Universes is infinite.
But regardless of M-theory being true or not, if our own Universe is infinite, then it is an absolute certainty that every structure or pattern in it must be duplicated an infinite number of times. That means galaxies, stars, planets, and us. If the Universe is infinite, then there is an infinite number of copies of you out there. There is also an infinite number of copies that are slightly different. And an infinite number of copies that are a bit more different, and so on. You get the idea.
Even if it turns out that our Universe is finite, and too small for probablity to demand duplicates, a perfectly mainstream theory of quantum mechanics proposes that every quantum event results in a splitting of the Universe into two or more concurrent states. If you like, one Universe where outcome A happened and one where outcome B happened. In this “many-worlds” theory, it’s impossible for Schrödinger’s cat to be both dead and alive at the same time: in one Universe it’s definitely dead, and in one, it’s definitely alive. (Note: Schrödinger was not cruel to cats in real life.)
“Many-worlds” envisages split after split after split, because everything that happens, happens the other way as well. In a finite Universe, that wouldn’t actually result in an infinite number of splits, but it would be a very large number, and most importantly there would be a version of the Universe reflecting every possible outcome since the beginning. (Of the Universe.) There is no conceivable way that these alternative Universes could ever be detected or could communicate with each other, so their existence is perhaps unprovable, a matter of faith if you like.
But I like the idea. In either the infinite Universe or the many-worlds one, there are different versions of me “out there”. When I’m disappointed in life or things go badly, I always think “Well, somewhere, it turned out differently. Somewhere, I wrote the hit song, won the prize, got the girl.”