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Is there any mathematical structure modelling parallel universes (multiverse)? If we established such structure, is it science or science-fiction?

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We do have such structure in place:

First, anything beyond the cosmological event horizon is effectively part of a different universe. An extension of that idea is the inflationary multiverse with bubble universes that can even have varying physical laws due to differently broken symmetries. String theory in turn adds its own flavour to that idea via the landscape multiverse.

While these multiverses are essentially just far away places, there are also theories featuring more exotic kinds of multiverses: One of them would be the brane multiverse of string theory where we can have literally parallel universes, another one the many-worlds interpretation of quantum mechanics.

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Yes, you know - the many worlds theory is one of interpretations of quantum mechanics - so you can use quantum physics equation there (Like a probability by Born rule - the probability here can have a little different meaning). But the possible experiments what we would scientifically describe are (yet?) only speculations (Maybe because Copenhagen interpretation became more popular.).

http://en.wikipedia.org/wiki/Many-worlds_interpretation#Comparative_properties_and_possible_experimental_tests

If you mean another universes like a another dimensions we can calculate this by quantity of dark matter in space.

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One that is particularly interesting:

In a paper published in Physical Review X, physicists Michael Hall, Dirk-André Deckert, and Howard M. Wiseman have proposed a new view of quantum mechanics that may be testable in a way that could prove that it alone is the correct interpretation. They call it the Many Interacting Worlds approach to quantum mechanics. The view they're proposing is that an infinite number of universes exist, each ruled by classical physics (i.e. no quantum mechanics!) and that phenomena that we see as quantum mechanical arise because the universes can interact with each other.

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