Caption: A cartoon the universe of the eternal inflation paradigm which is a generalization of the (minimal) inflation paradigm.

Note eternal inflation and inflation are just synonyms for, respectively, the eternal inflation paradigm and the inflation paradigm.

Eternal inflation posits whole universe consisting of a (background) false-vacuum universe and infinitely many pocket universes.

The whole universe and false-vacuum universe are eternal and infinite.

The pocket universes are NOT eternal (though some may live forever after coming into existence) and are NOT infinite.

The whole universe of the eternal inflation paradigm is a version of the multiverse paradigm. We will NOT elaborate on the multiverse paradigm in general.

Note eternal inflation and the multiverse are both highly speculative theories. The inflation paradigm in itself has a measure of robustness: it's resisted falsification since introduced in 1979 (see Wikipedia: Starobinsky inflation: History) though it has undergone considerable evolution.

Features:

1. The term multiverse just means the universe as whole in the case where said universe as whole has regions---called pocket universes---that differ in properties and said pocket universes give the appearance of being themselves the universe as whole to observers who are embedded deep in them. Those observers have "observable universes" smaller than their pocket universes.

   We, of course, are one of those observers.

2. Many kinds of multiverse are considered (see Wikipedia: Multiverse). But here we will just consider the eternal inflation version of the multiverse which is the most commonly thought of one thought of in cosmology and call it "the multiverse".

   As aforesaid eternal inflation is also a version of inflation. But inflation and multiverse are different paradigms.

   Some of the features of eternal inflation are rather undefined since eternal inflation probably has its own versions.

3. Eternal inflation posits that the whole universe consists of pocket universes embedded in a background universe which (following inflation cosmology jargon) can be called the false-vacuum universe---as labeled twice in the image, rightly spelt in the upper right and misspelt in the lower left.

   The universe is eternal and infinite---which solves the problem of before/after/outside of: i.e., there NO boundary conditions in spacetime to specify.

4. The observable universe is a spherically-symmetric region centered on us (roughly speaking, the Milky Way) which is embedded in one pocket universe which is our pocket universe.

5. Note that the image illustrates pocket universes embedded in the false vacuum universe.

   NO consensus theory tells us if pocket universes are spherical, if they have sharp edges, what their relative sizes are, what there relative separations are, or if they ever interact.

   Recall, the observable universe is embedded in our pocket universe, and so we CANNOT directly observe outside of it.

6. The false vacuum of the false-vacuum universe. is full of a quantum field (but there is NO consensus theory of what that quantum field is) in a metastable state at every point (i.e., is locally metastable).

   Metastable means stable against small enough perturbations, but large enough perturbations will cause the state to change irreversibly at least on some time scale.

7. To elaborate origin of origin of pocket universes from the false vacuum universe, see Cosmology file: inflation_paradigm.html.

8. Can we ever prove that there is eternal inflation or some other inflation that gives a multiverse?

   Two possible pieces of evidence for the multiverse have been discussed (see, e.g., Livio, M. 2013, How Can We Tell If a Multiverse Exists?):

   1. We discovery a TOE which explains everything we observe perfectly and this TOE inescapably predicts a multiverse.

      In this case, we would be forced to conclude the multiverse may well exist even though direct observations may never be obtained.

      Of course, maybe TOE would rule out the multiverse absolutely.

   2. It could be that the observable universe does straddle the boundary of our pocket universe or even include a piece of the another pocket universe.

      If so, observations in the future may detect the boundary or other pocket universe. This would be some proof of the multiverse.

      However, at present all observations are consistent with the observable universe as having homogeneity and isotropy when viewed on a sufficiently large scale: i.e., as obeying the cosmological principle. For an explication of the cosmological principle, see Cosmology file: observable_universe_cosmological_principle.html.

      You do have to look on a very large scale. Circa 2022, the thinking is that the cosmological principle scale ∼ 400 Mpc = 0.4 Gpc (see Wikipedia: Cosmological principle: Violations of homogeneity).

      Note the comoving radius of the observable universe = 14.25 Gpc = 46.48 Gly (current value) according to the Λ-CDM model (AKA the concordance model) of the observable universe (see Wikipedia: Observable universe). So the cosmological principle scale ∼ 400 Mpc = 0.4 Gpc is much smaller than the scale of the observable universe.

      Note, however, the largest cosmic structures are ∼ 1 Gpc (see Wikipedia: List of largest cosmic structures). But these may be statistical fluctuations and NOT violations of the cosmological principle scale ∼ 400 Mpc = 0.4 Gpc (see Wikipedia: Cosmological principle: Violations of homogeneity).

   Note that NEITHER of these two possible evidences are sufficient to prove the multiverse to most people's satisfaction.

9. Some people have argued that the multiverse should be NOT be considered a scientific theory at all since they argue does NOT satisfy falsifiability.

   To digress, falsifiability is the philosophy of science rule, that a scientific theory should make predictions that if they fail, the scientific theory has be proven to be wrong: i.e., it has be been falsified.

   Actually, there has been a lot of discussion about falsifiability, but most scientists probably agree that treated with a great deal of flexibility, it is a useful rule. Flexibility: To incompletely explicate flexibility:

   1. A theory that is in principle falsifiable even if NOT in practice currently should still be judged a a scientific theory if one can imagine testing sometime in the future.
   2. A theory that make predictions that can never imaginably be tested, but makes many that can, is judged scientific theory. General relativity is arguably in this category.
   3. A theory that has passed all falsification tests one can think of should still be judged a scientific theory even though it is no longer falsifiable.

   What most scientists probably agree on is that a theory whose proponents explain away any failed prediction with ad hoc hypotheses or false arguments is a theory which is no longer a scientific theory in practice even if it once was. Such a theory is now fruitless and even a fraud or a crank's delusion.

   For example, philosopher of science Karl Popper (1902--1994) argued that Marxism as it had come to be promoted was no longer a scientific theory (see Wikipedia: Karl_Popper: Falsifiability and the problem of demarcation).

10. What of the multiverse? Is it falsifiable?

    Yours truly's short answer is that the multiverse has passed one significant falsification test, but may be the only one anyone can ever think of. So multiverse is in scientific Limbo.

    For an under construction discussion of the multiverse and falsification, see Cosmology file: inflation_eternal_falsifiable.html.