Thank you Chronos for the prompt reply.
I was actually hoping for a different answer, as yours makes it a little more difficult for me to understand the current cosmological paradigm.
Talking about the Universe being infinite seems popular right now, with Max Tegmark talking about it with an infinite number of duplicate Earth's, and with NASA having a web page talking about it as well. There seem to a number of scientists who talk as if the Universe being infinite is a good assumption. Anyway, the following is a list of some of the points that I think reflect the current scientific consensus, although I cannot find any knowledgeable scientist discussing them.
I would look forward to any corrections or comments.
o The FRW metric allows for three solutions to the GR equations. Only one, the spherical solution, result in a Universe that is of finite volume. The other two, the flat and hyperbolic, are both infinite in size.
o Inflation results in a Universe that is still of finite volume, but is large enough to appear flat locally.
o The infinite solutions, the actual flat Universe and the hyperbolic Universe, are infinite in size at the time of the BB. This is quite surprising to me, as I have never heard of discussion of this point, and only came across it in an exercise in a textbook. I do not recall seeing it here in PF, for example, but you probably do.
o My "visualization aid" of thinking of the infinite BB as an unbounded two dimensional sheet, very hot and dense, is a legitimate description of the event.
o The current state of knowledge in Astronomy is that the Universe is close to flat, yet it is still impossible to tell which, if any, of the above three solutions to GR apply. That is we still do not know if the the Universe is flat and infinite, or near-flat and not.
Most of my life I have heard of the BB described as either a point, or Planck length, which is dense but finite, and then which expands. This is substantially different then a sheet with an infinite mass and dimensions, which then expands. It would also seem to result in a different set of theories about the origin of the BB. So, the following question seem relevant.
o The current discussion of the Hartle-Hawking theory of the origin of the BB talks of uncertainty and quantum fluctuations. Do the Uncertainty Equations allow for a quantum fluctuation that is infinite in both size and energy?
o If not, does that inability to use the Uncertainty Principle in Cosmology negate all such theories in the case that the Universe is either flat or hyperbolic?
There would seem to be quite a few questions about a BB with infinite size and mass, however I am just trying to find out if I am on a Snipe Hunt here.
Allow me to thank you for your many informative postings over the years, it has been an fascinating education.
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