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The theory of the Multiverse is what Parallel Universes is called.

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 thoery 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. AdS/CFT correspondence suggests that even quantum gravity is unitary. Dechonerence experimentally verified. Mathmatically, this is the simplest model.

This means that any universe you can conceive of exists, somewhere/somewhen. One where your President, died at birth, became a Teacher, serial killer, journalist, etc.

Level 4: Other mathematical Structures.

Features: Different funamental equations of physics.

Assumption: Mathematical existence = physical existence.

Evidence: Unreasonalbe 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!