Reference:
Elbaz et al. Quasar induced galaxy formation: a new paradigm? Astronomy and Astrophysics, 2009; 507 (3): 1359 DOI: 10.1051/0004-6361/200912848
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Physicists have calculated the number of distinguishable universes to be 10^10^16. The idea of multiverse raises a different theory of the Big Bang. Instead of the producing a single uniform universe, multiple universes appear in uniform.
The Big Bang was essentially a quantum process which generated quantum fluctuations in the state of the early universe. After that, the universe then underwent a period of rapid growth called inflation during which these perturbations were "frozen", creating different initial classical conditions in different parts of the cosmos. Since each of these regions would have a different set of laws of low energy physics, they can be thought of as different universes. The actual number depends critically the way the universes are defined.
The limit of how many universes humans can observe is dependent on the properties of the oserver and not on the properties of the multiverse.
Reference: arXiv blog