The universe is not infinite, as proven by Olber's Paradox (see reference below for a full explanation).
In short, if the universe is infinitely large, and infinitely old, and has roughly uniform distribution of stars, then the infinite universe theory would be correct. However, we know that the universe does not fit all of these criteria, because space is black.
If it were infinitely old, infinitely vast, and had stars everywhere, then there would be no direction you could possibly look that did not have a star in that direction, in some distance - possibly very large, but still a finite one... This means that every possible speck of sky would be lit by a star in that direction - it would therefore be luminous, and not dark as it is today.
Read the link below for a more in-depth description of Olber's Paradox.
Now what you're also talking about is parallel universes. There is not any way that we can think of today to detect and prove, or to conclusively disprove the existence of parallel universes. If there are an infinite number of parallel universes, there is a universe for every imaginable contingency - not just one in which you did not marry your husband, but one where everything is identical in every detail, except that you put two exclamation points after "insert any other person in here"
That is too far from testable to interest scientists at the moment. Science only deals in questions / postulations whose validity can be conclusively proven or disproved, so there isn't a whole lot of research being done on the existence of the parallel universe where you ate blackberry cobbler before going in to work this morning.
EDIT: Stephen Hawking used this idea as a sort of "solution" to his black hole information paradox, but I find it to be a bit of a cop-out.