There are at least 2 Scientific tests running now that are trying to prove or disprove the Multiverse. There are at least four types of different or "parallel universal theories" and they are:
Level 1: Regions Beyond our Cosmic Horizon
Features: Same laws of Physics, different initial conditions.
Assumptions: Infinite space, ergodic matter distribution
Evidence: Microwave background measurements point to a flat, infinite space, with large-scale smoothness.
This is the simplest mode.
These are ones, that because the Universe is endless, there are out "islands" of matter (like a different universe almost), so far away that we can never, ever see them from our Universe. They still technically exist "in" our universe, but for all intentions, they are so far away, they may as well be another universe. If this is correct, there are an infinite number of these other island universes in ours and because of that, the odds are near 100% that you exist out there on another Earth. Because their laws of nature are the same as ours, this almost must occur at some time.
Level 2: Other Post-Inflation Bubbles
Features: Same fundamental equations of physics, but perhaps different constants, particles and dimensionality.
Assumption: Chaotic inflation occurred.
Evidence: Inflation theory explains flat space (our universe appears FLAT), scale-invariant fluctuations, solves horizon problem and monopole problems and can naturally explain such bubbles.
Explains fine-tuned parameters.
These universes exist side-by-side with our own Bubble (balloon like) universe. We can never see them and may never be able to detect them, at least not now.
Level 3: The Many Worlds of Quantum Physics
Features: Same fundamental equations of physics, but perhaps different constants, particles and dimensionality. (Same as a Level 2)
Assumption: Physics Unitary
Evidence: Experimental support for unitary physics. link
/CFT correspondence suggests that even quantum gravity is unitary. Dechonerence experimentally verified. Mathematically, this is the simplest model.
This means that any universe you can conceive of exists, somewhere/some-when. One where your President, died at birth, became a Teacher, serial killer, journalist, etc.
Level 4: Other mathematical Structures.
Features: Different fundamental equations of physics.
Assumption: Mathematical existence = physical existence.
Evidence: Unreasonable effectiveness of math in physics. Answer Wheeler/Hawking question "why theses equations, not others?"
In this universe the properties of nature are different or may not even exist in some universes!
Personally, I recommend going to YouTube and searching for "parallel universes, michio kaku, multiverse and brane theory." Best of luck.