Well, the existence of parallel realities kind of grows out of quantum mechanics, and specifically a philosophy of QM known as the Many Worlds Interpretation. MWI is a usefull way of looking at certain phenomina, but it is an interpretation, and should not be confused with a "theory". I happen to think that this interpretation or "view" contains a self-contradiction and is therefore not valid.
As far as serious research, that is almost impossible with an interpretation. In fact, that's kind of the difference between an interpretation and a theory. A theory is something you can test, a veiw is not. Some modern physicists are trying to say that the creation of a quantum computer would prove the existence of parallel realities, but taking this as proof requires that one first accept certain assumptions that are by no means certain.