According to the holographic principle, there should be a physically-equivalent parallel universe that would exist on a distant bounding surface (the edge of the universe), in which everything about our universe is precisely mirrored.
What exactly does this mean?
Well, we live in a three dimensional universe. If you have a 3-dimensional region then the edge of that region would be a 2-dimensional surface. For example, if you have a solid rubber ball, the 3-dimensional object has a 2-dimensional spherical surface.
The holographic principle suggests that this surface would contain enough information to perfectly represent everything that takes place within it. Think of it kind of like a reflection on the surface (although this is only a useful analogy, the precise formulation of the holographic principle is a mathematical relationship based upon quantum physics).
If this highly-theoretical conjecture is true, then that means that our universe exists in two different forms, though those two universes are completely identical in every respect. As Brian Greene explains in his 2011 book, The Hidden Reality:
Our experiences here, and that distant reality there, would form the most interlocked of parallel worlds. Phenomena in the two - I'll call them Holographic Parallel Universes - would be so fully joined that their respective evolutions would be as connected as me and my shadow.