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The biggest problem with a multiverse theory is explaining consciousness, because you can come up with all the equations you want to say when the universe splits, how it splits, and whatever but it comes down to this question: why do we experience _this_ reality. I mean, assuming that splitting is involved, there's an infinite number of ourselves being created every moment, yet our consciousness chooses to follow one path and continuously at that.
In quantum mechanics, this is usually called 'many-minds' or 'many-worlds,' and the theory does very well in empirical predictions but falls into some problems when trying to explain why the splitting happens and how we experience it. If you're talking about time travel, it could be a convenient way to avoid paradoxes of going back in time. I can't say I'm too convinced that we live in a multiverse. It's so hard to have direct evidence of it.
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