One of the curious developments in cosmology in recent years has been the emergence of the multiverse as a mainstream idea. Instead of the Big Bang producing a single uniform universe, the latest thinking is that it produced many different universes that appear locally uniform.
One question that then arises is how many universes are there. That may sound like the sort of quantity that is inherently unknowable but Andrei Linde and Vitaly Vanchurin at Stanford University in California have worked out an answer, of sorts.
Their answer goes like this. The Big Bang was essentially a quantum process which generated quantum fluctuations in the state of the early universe. 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.
What Linde and Vanchurin have done is estimate how many different universes could have appeared as a result of this effect. Their answer is that this number must be proportional to the effect that caused the perturbations in the first place, a process called slow roll inflation, and in particular to the number “e-foldings” of slow roll inflation.
Of course, the actual number depends critically on how you define the difference between universes.
Linde and Vanchurin have applied some reasonable rules to calculate that the number of universes in the multiverse and have totted it up to at least 10^10^10^7. A “humungous” number is how they describe it, with no little understatement.
How many of these could we actually see? What’s interesting here is that the properties of the observer become an important factor because of a limit to the amount of information that can be contained within any given volume of space, a number known as the Bekenstein limit, and by the limits of the human brain.
Linde and Vanchurin say that total amount of information that can be absorbed by one individual during a lifetime is about 10^16 bits. So a typical human brain can have 10^10^16 configurations and so could never disintguish more than that number of different universes.
10^10^16 is a big number but it is dwarfed by the “humungous” 10^10^10^7.
“We have found that the strongest limit on the number of different locally distinguishable geometries is determined mostly by our abilities to distinguish between different universes and to remember our results,” say Linde and Vanchurin
So the limit does not depend on the properties of the multiverse but on the properties of the observer.