Yikes! The questions just get harder and harder! [img]/phpBB/images/smiles/icon_wink.gif[/img]

There's an April 2002 paper by one of the big guns of theoretical cosmology, Andre Vilenkin, which goes into the idea of eternal inflation.

In this paper Vilenkin first discusses the theoretical framework for an initial singularity nucleating via quantum processes from 'nothing'--a condition without the attributes of space or time. On page 10 of the paper he notes that while theory allows inflation to be eternal into the future, it appears that Arvind Borde, Alan Guth, and others have shown that the DeSitter equations do not allow a universe which is eternal into the past (I don't understand the theory, I have to take Borde's and Guth's word for it).

My statement that there is no sign of a beginning is, if their work is correct, wrong.

On the testablity of the eternal-into-the-future hypothesis, Vilenkin writes:

[Pedantic self-correction: Vilenkin is speaking of the testablity of the quantum-nucleation origin of a singularity, not the eternal-into-the-future part of inflation theory. Sorry.]

"There are also some bad news. In the course of eternal [into-the-future] inflation the universe quickly forgets its initial conditions. Since the number of thermalized regions [ie regions where the false vacuum has collapsed--DS] to be formed in an eternally inflating universe is unbounded, a typical observer is removed arbitrarily far from from the beginning and all memory of the initial state is completely erased. [Here of course Vilenkin is not talking about human memory, but about the 'memory' preserved in the universe through evidence like the cosmic background radiation.--DS] This implies that any predictions that quantum cosmology could make about the initial state of the universe cannot be tested observationally."

Now, as to the question above--what would be different in these these different 'thermalized' regions:

"The only case that requires special consideration is when there are some constants of nature, [alpha_j], which are constant within individual universes, but can take different values in different universes within the ensemble. (One example is the cosmological constant in models where it is determined by a four-form field.) In this case, the memory of the initial state is never completely erased, since the values for [alpha_j] are always equal to their initial values."

abstract in html, full paper in PDF.

So: perhaps one of the constants which might vary between 'thermalized' regions in Vilenkin's proposal for an eternally-inflating universe would be the 'dark energy' of the vacuum.

As far as the eternal-into-the-future inflation hypothesis goes, I don't see how separate regions, separate bubble-universes, could affect each other's expansion rate. It would appear that they are cut off from each other by an exponentially expanding gulf of false vacuum, and no conceivable signal--no force, no energy--could travel between them.

I'm not sure about the bubbles coalescing or colliding. One of the key concepts of the eternal-inflation set of hypotheses is that because the false vacuum expands at an exponential rate--doubling and redoubling its size in fantastically short time periods--and the bubbles only expand linearly (I think), then the bubbles of thermalized, 'collapsed' vaccum cannot all merge and fill the super-universe. What the likelihood of two bubbles merging would be, I just don't know.

<font size=-1>[ This Message was edited by: DStahl on 2003-02-10 01:21 ]</font>

<font size=-1>[ This Message was edited by: DStahl on 2003-02-11 17:13 ]</font>