First of all, scientists have confirmed that a "mirror" universe would look and behave just like ours. Antiprotons interact with each other just the way protons do. (In other words, we still don't know why the universe exists - why the big bang left a bit of one "side" of matter over).
Second of all, perturbations in the cosmic background radiation MAY demonstrate that our universe is just one pocket of expansion in something much larger, and other similar pockets exist - multiple universes, which may have slightly different laws of physics.
Put the two together and one has to wonder if there actually was an equal amount of what we call matter and what we call anti-matter in the Big Bang and it just blew out in different directions. Scientists are already looking for gamma radiation "boundaries" that might indicate where a matter universe and an anti-matter universe brush against one another.
(If this all gives you a headache - you are not alone!).