Why are multiple universes science?
First and perhaps most fundamentally they are because perhaps the most successful physical theory in existence (quantum theory, and in particular the non-relativistic quantum mechanics whence relativistic QFT, particle physics, etc., are derived) involves a description of physical systems which is at once utterly and completely deterministic (not to mention incredibly simple, by virtue of linearity) and probabilistic. The earliest multiverse theory did not originate from attempts to reconcile general relativity with quantum theory nor with any cosmological models nor fine tuning but rather the interpretation of the simplest description of the most fundamental interactions. By rejecting Born's rule and any similar projection postulate more generally, Hugh Everett III and those who developed his relative state interpretation into the various many-worlds theories seen today proposed instead that, even though in any and every experimental setting (or any setting, for that matter) only one of the possible outcomes yielded by quantum theory appears to be realized, this is because all outcomes are realized but each in a single universe.
Basically, quantum mechanics gives us a completely deterministic picture right up until we actually use it. Then we must encode, impose, and utilize a statistical structure into the theory and the measurement process. But we need not assume (so goes the argument) that this extra structure is required to describe physical processes/systems. Instead, some assert, we should take at face value the fact that quantum theory tells us the outcomes of physical processes and the fact that we interpret these probabilistically is because in any particular universe only one possible outcome is realized.
This is, of course, not the only way in which multiverse theories are part of theoretical physics, cosmology, etc. The idea of multiple universes in some cases really only means that there is a single universe, but because of e.g., expansion "parts" of the universe become so fundamentally isolated they are universes in and of themselves from a physical perspective. So sometimes it is simply a matter of semantics: we change what we mean by "universe", making the term apply to sufficiently distinct, isolated realms of the whole of physical reality whilst applying the term "multiverse" to the sum of all such realms (what formerly and in many cases still even multiverse proponents would admit it meant by "universe").
Multiple universes are a natural consequence of attempts to unify general relativity and quantum mechanics. Some models *are* testable because they have gravitational interactions between universes. There was even one (discredited) report of anomalies that could be attributed to such interaction.
To the extent these models are testable, they are clearly science.
Not exactly. They are not testable (in most cases, they are postulated because they cannot even in principle be tested, whence comes the idea that it is appropriate to speak of multiple universe- realms so isolated and enclosed from what we would call the universe that it can be helpful or informative to speak of them as universes themselves. Put differently, they are tested mathematically, not empirically and in many cases cannot ever be tested empirically.
Also, there are not really any natural consequences of attempts to unify general relativity and quantum mechanics because there are no known natural ways to do this really. Also, most of the cosmological multiverse theories are not due to quantum gravity but to assumptions about what it might be. In fact, sometimes quantum gravity doesn't play any role at all. General relativity and expansion yield certain multiverse cosmologies without any quantum theory of gravity.
We can't test gravitational interactions among universe because
1) We can't test any interaction among physical realms that are called universes because by definition they are so distinct as to prohibit any possible interactions
2) We have no way of testing any gravitational effects that involve quantum theory as in quantum descriptions of spacetime, not only is spacetime affine but gravity is a field mediated by a postulated "particle" rather than spacetime curvature
3) Underdetermination of would-be theory by data
From the physics point of view, though, the question of fine tuning is an added benefit. The *real* issue is the unification of GR and QM.
Not necessarily. Multiverse cosmologies are proposed sometimes specifically because they solve the fine-tuning problem. They are postulated to explain why our universe has the properties it does- namely, any would-be finely tuned parameters are not finely tuned but are one realization out of many actual realizations.
"Despite the growing popularity of the multiverse proposal, it must be admitted that many physicists remain deeply uncomfortable with it. The reason is clear: the idea is highly speculative and, from both a cosmological and a particle physics perspective, the reality of a multiverse is currently untestable. Indeed, it may always remain so, in the sense that astronomers may never be able to observe the other universes with telescopes a and particle physicists may never be able to observe the extra dimensions with their accelerators...
For these reasons, some physicists do not regard these ideas as coming under the purvey of science at all. Since our confidence in them is based on faith and aesthetic considerations (for example mathematical beauty) rather than experimental data, they regard them as having more in common with religion than science. This view has been expressed forcefully by commentators such as Sheldon Glashow [22], Martin Gardner [23] and George Ellis [24], with widely differing metaphysical outlooks. Indeed, Paul Davies [25] regards the concept of a multiverse as just as metaphysical as that of a Creator who fine-tuned a single universe for our existence."
From the editor's introduction to Carr, B. (2007). (Ed.).
Universe or Multiverse? Cambridge University Press.