Quantum fluctuations of the metastable false vacuum

[PeterDonis]

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.

Sean Carroll wrote an excellent article a while back that explains what's going on here:

http://www.preposterousuniverse.com/blog/2010/02/22/energy-is-not-conserved/

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).

 

[PeterDonis]

I don't recall anything in the lectures I've seen considers any space "infinite"

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.

 

[nikkkom]

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.

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.

Though each bubble may have different constants and parameters (like G, h, and c)

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.