parallel universe

from The American Heritage® Dictionary of the English Language, 5th Edition.

• noun A universe, especially one of an infinite set of identical universes, hypothesized in some interpretations of quantum mechanics to exist along with our own universe, obeying the same physical laws, but each in a different quantum mechanical state with no possibility for the transfer of information between universes.
• noun A universe hypothesized in some cosmological models to exist along with our own universe, possibly obeying different physical laws and having the potential for the transfer of information between universes.

from Wiktionary, Creative Commons Attribution/Share-Alike License.

• noun sciences, science fiction A universe that exists separately alongside another universe.