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(...) the idea that the universe is perhaps one of infinitely many is derived from current theories like quantum mechanics and string theory.
String theory
(...) String theory is one of our most, if not the most promising avenue to be able to unify quantum mechanics and gravity. This is notoriously hard because gravitational force is so difficult to describe on small scales like those of atoms and subatomic particles – which is the science of quantum mechanics. But string theory, which states that all fundamental particles are made up of one-dimensional strings, can describe all known forces of nature at once: gravity, electromagnetism and the nuclear forces.
However, for string theory to work mathematically, it requires at least ten physical dimensions. Since we can only observe four dimensions: height, width, depth (all spatial) and time (temporal), the extra dimensions of string theory must therefore be hidden somehow if it is to be correct. To be able to use the theory to explain the physical phenomena we see, these extra dimensions have to be “compactified” by being curled up in such a way that they are too small to be seen. Perhaps for each point in our large four dimensions, there exists six extra indistinguishable directions?
Inflation
(...) During the very early universe, before the Big Bang, the universe underwent a period of accelerated expansion called inflation. (...) a consequence of this theory is that there must be other parts of the universe that are still accelerating. However, due to the quantum fluctuations of space-time, some parts of the universe never actually reach the end state of inflation. This means that the universe is, at least according to our current understanding, eternally inflating. Some parts can therefore end up becoming other universes, which could become other universes etc. This mechanism generates a infinite number of universes.
By combining this scenario with string theory, there is a possibility that each of these universes possesses a different compactification of the extra dimensions and hence has different physical laws. (...)
Testing The Theory
The universes predicted by string theory and inflation live in the same physical space (unlike the many universes of quantum mechanics which live in a mathematical space), they can overlap or collide. Indeed, they inevitably must collide, leaving possible signatures in the cosmic sky which we can try to search for.
The exact details of the signatures depends intimately on the models – ranging from cold or hot spots in the cosmic microwave background to anomalous voids in the distribution of galaxies. Nevertheless, since collisions with other universes must occur in a particular direction, a general expectation is that any signatures will break the uniformity of our observable universe.
These signatures are actively being pursued by scientists. Some are looking for it directly through imprints in the cosmic microwave background, the afterglow of the Big Bang. However, no such signatures are yet to be seen. Others are looking for indirect support such as gravitational waves, which are ripples in space-time as massive objects pass through. Such waves could directly prove the existence of inflation, which ultimately strengthens the support for the multiverse theory.
Whether we will ever be able to prove their existence is hard to predict. But given the massive implications of such a finding it should definitely be worth the search.