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:
We, of course, are one of those observers.
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.
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.
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.
Metastable means stable against small enough perturbations, but large enough perturbations will cause the state to change irreversibly at least on some time scale.
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?):
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.
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).
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:
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).
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.