Fragments

From inflation_region_cartoon.html

What does the inflated region (i.e., the pocket universe) look like from the outside?
It may look like a black hole, but because of the internal expansion (i.e., the expansion of the universe), a black hole without a singularity at the center: i.e., a black hole with a difference (SC-23).
Outside it may be Hamlet's "nutshell.'' See the figure below local link / general link: hamlet_edwin_booth.html).

If this is literally true, stuff from outside could fall into our pocket universe, but CANNOT get out---but where it would arrive and how would it appear and what would it be?
Image 3 Caption: Probably the most talked of inflation theory is called eternal inflation which is an inflation cosmology version of the multiverse.
Actually, there are probably many versions of eternal inflation, but to avoid tediousness, we just refer to eternal inflation as one theory.
In eternal inflation, observable universe is deeply embedded in a pocket universe since we observe NO signs of the boundary of the pocket universe.
There are infinitely many pocket universes that are embedded in the the false-vacuum universe. The pocket universes all arise from quantum fluctuations in the false-vacuum universe.
The pocket universe and the false-vacuum universe together constitute the whole universe.
The cartoon in Image 3 shows the boundaries of the pocket universes as sharp. But they may be gradual.
In fact, there may be NO boundaries on the inside. The pocket universes could be some kind of black hole universes: i.e., they are the insides black holes.
Stuff from outside can fall in, but nothing can get out. But where does stuff appear on the inside?
The pocket universes may have different PHYSICAL CONDITIONS (i.e., physics itself or initial conditions). For example, fundamental constants may have different values in different pocket universes.
If PHYSICAL CONDITIONS do vary, then they must be set randomly from some distribution.
The PHYSICAL CONDITIONS of our pocket universe are then what they are by the anthropic principle: fine-tuned enough for life as we know it, but NOT overly fined-tuned. Our pocket universe is thus a fine-tuned universe: i.e., fine-tuned for life as we know it.
Most pocket universe might lifeless and rather boring.
If the PHYSICAL CONDITIONS of our pocket universe were overly fine-tuned for life as we know it, then almost certainly are determined by some logic of reality and NOT by an eternal inflation with random PHYSICAL CONDITIONS sets the PHYSICAL CONDITIONS.
Thus, eternal inflation with randomly set PHYSICAL CONDITIONS passes one significant falsification test: PHYSICAL CONDITIONS we observe are
NOT overly fine-tuned for life as we know it.
This may be the only falsification test it passes---but it is a significant falsification test.
UNDER CONSTRUCTION BELOW

From inflation_false_vacuum_decay.html

The pocket universes are usually thought to have somewhat different physics (e.g., different values for fundamental physical constants, different elementary particles, and maybe other things).
If physics does vary pocket universes ordinary physics (atomic physics, nuclear physics, and maybe quantum chromodynamics: the physics of quarks) may be emergent physics---an accident of the way our pocket universe was initiated by its initial random quantum fluctuation.
However, our most fundamental physical laws (e.g., quantum mechanics, quantum field theory, general relativity as macroscopic scale emergent theory from quantum gravity, theory of everything (TOE), thermodynamics statistical mechanics, TOE-Plus) are assumed to be constant (but NOT their fundamental physical constants, etc.) or we have NO guidance at all for the universe well beyond the observable universe either in space or time. We would NOT even be able to speculate about the "beyond"---except in philosophy.
At least in some fraction of pocket universes where the physics is rich enough all kinds of the complex structures can develop like life as we know it.
Note we do NOT know what the most fundamental physics is.
But we have a name for it anyway: the theory of everything (TOE).
This is NOT a good name in yours truly's view since it is NOT a theory of everything---but no one ever listens to yours truly.
Some theorists think that string theory (which is a candidate for TOE) could accommodate wildly varying ordinary physics between the pocket universes, but it may NOT (see, e.g., Livio, M. 2013, How Can We Tell If a Multiverse Exists?).
The false-vacuum universe is usually thought of as governed by general relativity (GR). In which case, it maybe a perpetually expanding universe or contracting universe on large scales.
However, the density of mass-energy in the false vacuum may be so high that quantum gravity governs false-vacuum universe. Since we do NOT have an established quantum gravity theory, referring to quantum gravity may mean we know nothing much about the false-vacuum universe.
Note the pocket universes may NOT be eternal. Some titanic event may "evaporate" them or contract them back to the false-vacuum state.
On the other hand, maybe they just expand forever or eventually become static embedded in the also expanding forever false-vacuum universe.
If the false vacuum also expand forever, it may keep most pocket universes causally disconnected (i.e, they never affect each other in any way) forever.
However, wormholes actually exist, they may make causal connections between the pocket universes---but idea is highly speculative.
The whole universe has local evolution due to the formation of pocket universes, but does it evolve overall (i.e., have global evolution).
Yours truly thinks that the speculation is no, it does NOT evolve globally.
Does its entropy increase? If does NOT evolve globally, no. Unless as some have theorized (e.g., Sean Carroll (1966--)) ever increasing entropy is a fundamental fact of the whole universe.
Two key points about inflation:
1. A pre-inflation region could all have been in thermodynamic equilibrium (or very nearly) and the inflation maintains that.
2. Inflation could stretch space such that a pocket universe has Euclidean geometry (AKA flat geometry).
The observable universe did start in nearly exact thermodynamic equilibrium (as we can tell from the cosmic microwave background (CMB)) and is has Euclidean geometry (AKA flat geometry) to within uncertainty.
Thus, inflation explains two important features of the observable universe. This has always been a strong argument for the inflation paradigm, but NOT for any particular version of inflation.