There is no solid math or physics which supports time travel. There are a lot of cases where people claim to have found some loophole or another in the impossibility proofs for time travel, sketching out a model that looks plausible at first glance, but they all end up postulating some blatantly non-physical entity somewhere along the way (i.e. cosmic strings, negative energy density, ... - I've gotten my hopes up quite a few times).

Speculating about parallel universes is a different story - even if they exist, we can't travel to them, so there is no sense in claiming that we can somehow harness their power. It's a philosophical question, not a physical one. In contrast, the rules of quantum mechanics (when phrased in terms of density matrices, at least) only describe things we can actually measure and observe, and people actually do test every single aspect of the predictions quantum mechanics makes.