For most of the 20th century, scientific thought was dominated by the idea of the uniformity of the universe and the uniqueness of laws of physics. Indeed, the cosmological observations indicated that the universe on the largest possible scales is almost exactly uniform, with the accuracy better than 1 in 10000.
A similar situation occurs with respect to the uniqueness of laws of physics. We knew, for example, that the electron mass is the same everywhere in the observable part of the universe, so the obvious assumption was that it must take the same value everywhere, it is just a constant of nature. For a long time, one of the great goals of physics was to find a single theory that would unify all fundamental interactions and provide an unambiguous explanation for all known parameters of particle physics.
Thirty years ago, a possible explanation of the uniformity of the universe was found. The main idea was that our part of the world emerged as a result of an exponentially rapid stretching of space, called cosmic inflation. Then all "wrinkles" and non-uniformities of space are stretched out and disappear. The universe becomes incredibly smooth. Add a little bit of quantum fluctuations, stretch them, the resulting uniformity becomes just a little bit less perfect, and galaxies emerge.
At first, inflationary theory looked like an exotic product of vivid imagination. But thanks to the enthusiastic work of thousands of scientists, many predictions of this theory have been confirmed by observations. And if the theory is correct, we finally have a scientific explanation of why the world is so uniform.
But inflation does not predict that this uniformity must extend beyond the observable part of the universe. To give an analogy, suppose the universe is a surface of a big soccer ball consisting of black and white hexagons. If we inflate it, the size of each white or black part becomes exponentially large. If inflation is powerful enough, those who live in a black part of the universe will not ever see the white part, they will believe that the whole universe is black, and they will try to find a scientific explanation why it cannot have any other color. Those who live in a white universe will never see the black parts and therefore they may think that the whole world must be white. But both black and white parts may coexist in an inflationary universe, without contradicting observations.
In the example given above, we were talking about black and white. But in physics, the number of different states of matter (the number of "colors") can be exponentially large. The best candidate for the "theory of everything" that is presently known to us is string theory. It can be successfully formulated in space-time with 10 dimensions (9 dimensions of space, and 1 time). But we live in the universe with 3 dimensions of space. Where are other 6? The answer is that they are compactified, squeezed into something so small that we cannot move in these directions, which is why we perceive the world as if it were 3-dimensional.
From the early days of string theory, physicists knew that there are exponentially many different ways to compactly the extra 6 dimensions, but we did not know what can prevent the compactified dimensions from blowing up. This problem was solved about 10 years ago, and the solution validated the earlier expectations of the exponentially large number of possibilities. Some estimates of the number of different options are as large as 10500. And each of these options describes a part of the universe with a different vacuum energy and different types of matter.
In the context of the inflationary theory, this means that our world may consist of incredibly large number of exponentially large "universes" with 10500 different types of matter inside them.
A pessimist would argue that since we do not see other parts of the universe, we cannot prove that this picture is correct. An optimist, on the other hand, may counter that we can never disprove this picture either, because its main assumption is that other "universes" are far away from us. And since we know that the best of the theories developed so far allow about 10500 different universes, anybody who argues that the universe must have same properties everywhere would have to prove that only one of these 10500 universes is possible.
And then there is something else. There are many strange coincidences in our world. The mass of the electron is 2000 times smaller than the mass of the proton. Why? The only known reason is that if it would change few times, life as we know it would be impossible. The masses of the proton and neutron almost coincide. Why? If one of their masses would change just a little, life as we know it would be impossible. The energy of empty space in our part of the universe is not zero, but a tiny number, more than a hundred orders of magnitude below the naive theoretical expectations. Why? The only known explanation is that we would be unable to live in the world with a much larger energy of vacuum.
The relation between our properties and the properties of the world is called the anthropic principle. But if the universe were given to us in one copy, this relation would not help. We would need to speculate about the divine cause making the universe custom built for humans. Meanwhile, in the multiverse consisting of many different parts with different properties, the correlation between our properties and the properties of the part of the world where we can live makes perfect sense.
Can we return back to the old picture of a single universe? Possibly, but in order to do it, three conditions should be met: One should invent a better cosmological theory, one should invent a better theory of fundamental interactions, and one should propose an alternative explanation for the miraculous coincidences which we just discussed.