Is it possible to ignore that though ? I knew that is not possible but I was interested in the thought experiment. I need an answer to that so I can have a better visualization on the matter at hand. I don't know how should I look at this whole issue and these type of thought experiments might give me the answer.

What about creating a wormhole from the bubble of spacetime B to somewhere in spacetime A ? Could that work as a possible premise for my thought experiment ?

But how time would "hook up" through the wormhole between B and A would depend on where you chose to "put" the wormhole mouths in the two spacetimes; there is no way to extract a unique prediction for that from the laws of physics. So a thought experiment based on this premise would not tell you anything you didn't put into it in the first place.

The more general answer to the question I think you are asking is that there is no well-defined relationship between "time" in the two spacetimes A and B.

I come back to this point for a clarification. I failed to raise this obvious point earlier. What about spacetimes that are not exponentially expanding ? In such a case, are there any reasons why light from spacetime A would not enter spacetime bubble B ?
And one further clarification on the application of the B.G.V. theorem. If memory serves, Alexander Vilenkin said that if quantum fluctuations are not wild enough to invalidate classical spacetime, the theorem still holds. This makes it sound like the theorem applies to pretty much any expanding spacetime. Someone pointed out to me though that the theorem does not imply a beginning of spacetime, merely that inflationary physics is not enough to provide us with a full picture of the Universe.

Also, what does "classical spacetime" mean ? I ask this because Alexander Vilenkin says that invalidating this kind of spacetime might have implications on our very notions of causality.

In that case there is no such thing as the "bubble" we have been discussing.

Yes, because there are no "bubbles" in this case. See above.

That's my understanding; but AFAIK the applicability of the theorem to whatever model actually ends up describing our actual universe is still an open question.

It means spacetime as modeled by GR, as a 4-dimensional manifold with a locally Lorentzian metric. When he talks about quantum fluctuations and whether or not they make classical spacetime "invalid", he is talking about whether spacetime modeled as a 4-dimensional manifold is exact or only an approximation, and if the latter, at what point does the approximation break down. This is also an open question--it is one of the key questions that the various proposed theories of quantum gravity are trying to address.

Whether this will end up being an issue is also an open question.

Is it possible for an infinite and non-expanding spacetime to start expanding ? Is it reasonable for me to assume that if it can do that, only regions of the said spacetime will start expanding and not the "whole" thing ? What mechanisms have been proposed to facilitate this expansion ? I assume the de-Sitter space is an example of an infinite spacetime that stars expanding for some reason and produces these bubbles ?

The question doesn't make sense. Spacetime doesn't change; it is a 4-dimensional geometric object that already contains everything that happens in the entire history of the universe. So it can't "start" doing something.

Expansion by itself doesn't need a "mechanism"; it's just inertia--things were moving apart in the past so they keep moving apart.

Accelerated expansion, the kind that is seen in de Sitter spacetime, is due to the presence of a positive cosmological constant. There is no other "mechanism".

No; de Sitter spacetime extends infinitely into the past and the future, and is "expanding" everywhere (when that term is properly defined--see below). The "bubbles" are not produced by spacetime itself, but by some kind of field in the spacetime that undergoes a transition.

To clarify the term "expanding": what this actually means, in technical terms, is that we can find a family of timelike geodesics whose expansion scalar is positive. Since this is an "A" level thread, you should know what that means; but if you don't, see here for a start:

I forgot to ask but is the Universe created in this paper a zero-energy one ? And do we know if our Universe is a zero-energy one or is that question still unanswered ?

Within the theory of Eternal Inflation, it is said that a quantum fluctuation of some sort at some "point in the meta-stable false vacuum space" caused the false vacuum to decay out to a lower vacuum energy and form bubbles with matter and photons. Though each bubble may have different constants and parameters (like G, h, and c), the implication is that each false vacuum (including the so called meta-space) has at least some common physics such as quantum fluctuations, expansion (perhaps), space, vacuum energy, time, and apparently the uncertainty principle.

Is this right? Are there "intrinsic laws" ?

Also, I don't recall anything in the lectures I've seen considers any space "infinite"; just sometimes growing really fast and really big, but not infinite. I doubt infinity actually exists in nature, only as a concept. But, I'm often wrong. (

I saw just yesterday an interview with Lawrence Krauss, the cosmologist, say that he considers the universe to have overall zero energy. His reasoning was that the expansion does work. Also, as vacuum energy is added, so is gravity added which is a negative energy. Not sure I fully understand.

Here is the key quote from the article for your question:

We all agree on the science; there are just divergent views on what words to attach to the science. In particular, a lot of folks would want to say “energy is conserved in general relativity, it’s just that you have to include the energy of the gravitational field along with the energy of matter and radiation and so on.”

Krauss is one of the "folks" Carroll is describing here. Carroll makes a different choice: he prefers to say that energy is not conserved in GR in a spacetime which is not stationary ("stationary" is the technical term for a spacetime like the one describing our universe as a whole, where there is no way to pick out a notion of "space" that does not change with time). He explains his reasons for preferring his choice over Krauss's choice in the article. But both are describing the same physics; they're just choosing different ways of doing it in ordinary language. Ultimately, that's why ordinary language isn't a good way to describe physics if you really want to understand it; you have to look at the math (and Krauss and Carroll are both describing the same math).

Our best current model of the universe is spatially infinite. But there is enough margin of error in our observations that it's still possible that the universe is not actually spatially infinite, just really, really large. Both kinds of models are mathematically consistent, so the only way we have to decide between them is by making more and more accurate measurements.

My understanding is that if you pick any point in a metastable vacuum phase and observe what happens to it, it will inevitably decay into a stable phase (by either nucleating a bubble, or by being swept up by an expanding bubble nucleated nearby).

However, since metastable phase is inflationary, the _volume_ of the space which has not decayed yet is always larger than the one which decayed.

The key word here is "may". There may be just two phases - one metastable and one stable. Or there may be many different stable phases with equal energy. It depends on the details of the theory. So far inflationary theories are not narrowed down to just one, well-developed theory, so we don't know whether there is one, or many stable vacuums.