On 11/10/2017 10:01 PM, agrayson2...@gmail.com wrote:
On Friday, November 10, 2017 at 2:16:04 PM UTC-7, Brent wrote: On 11/10/2017 1:01 PM, agrays...@gmail.com <javascript:> wrote:On Friday, November 10, 2017 at 12:19:05 PM UTC-7, Brent wrote: On 11/10/2017 4:06 AM, Alan Grayson wrote:On Thu, Nov 9, 2017 at 10:32 PM, Brent Meeker <meek...@verizon.net> wrote: On 11/9/2017 9:15 PM, Alan Grayson wrote:On Thu, Nov 9, 2017 at 10:05 PM, Brent Meeker <meek...@verizon.net> wrote: On 11/9/2017 8:55 PM, agrays...@gmail.com wrote:On Thursday, November 9, 2017 at 8:00:45 PM UTC-7, Brent wrote: On 11/9/2017 6:23 PM, Alan Grayson wrote:The difference between spatially flat and asymptotically flat for a huge universe would be virtually impossible to distinguish by measuring the sum of angles in a triangle. Moreover, I don't see how spatially flat can have nothing to do with extent, since in applying Euclidean geometry we surely seem to be dealing with an infinitely extended plane. TIA.Not necessarily. You could have periodic boundary conditions. But most cosmologists do assume the universe is infinite in spatial extent. Of course the flatness isn't measured by triangulation. It's measured by comparing the spatial spectrum of the CMB variations to model predictions with different mass densities. https://arxiv.org/pdf/astro-ph/0004404 <https://arxiv.org/pdf/astro-ph/0004404> Brent However flatness is measured, the criterion still seems Euclidean and hence infinite in extent if one believes the triangle measured has combined angles of 180 degrees. And I don't see how this is distinguishable from asymptotically flat for a huge but finite universe.It's not. That's my point. No way of distinguishing flat from asymptotically flat for a huge universe, so the assumption of infinite spatial extent by cosmologists seems unwarranted. But as you note below, the universe could have begun with infinite spatial extent. But ours didn't AFAIK. It began as astronomically tiny and expanded via inflation.But you don't know that. According to Einstein's equations the visible part of the universe started at /*zero*/ size. Of course no one takes that entirely seriously since at very small distances quantum mechanics must invalidate Einstein's equations. Brent If you're invoking QM, aren't you conceding it started out very small, if not exactly zero size? So it seems more plausible to assume it started out very small, surely not infinite. But according to your previous statements and those that I have read by cosmologists, the assumption of infinite spatial extent is generally accepted and IMO unwarranted.If it's flat or has negative curvature then the equations imply it's infinite or perhaps periodic (no matter what the scale factor is). If the curvature is positive then it's finite and closed and the scale factor can be taken to be the radius, so it indeed starts small in the absolute sense. Atkatz and Pagels showed that only FRW universes that are closed (positive curvature) or De Sitter (flat with a positive cosmological constant) can "tunnel out of nothing". http://www.quantum-gravitation.de/media/99f63994b9064eb6ffff8004fffffff2.pdf <http://www.quantum-gravitation.de/media/99f63994b9064eb6ffff8004fffffff2.pdf> So most cosmologists liked the closed universe model, until it was found that expansion is accelerating. So now more of them look to some modification of the De Sitter space universe. Brent Modification of De Sitter will be flat and therefore open. I find the open universe model in contradiction to the finite age of the universe. Is this unreasonable?Well, if you have an infinite universe, and toward the past it is scaled by a factor a, and a->0 does the universes size go to zero?Why is the closed universe model less favored when it was discovered that expansion is accelerating?Because the De Sitter universe that can "tunnel from the vacuum" automatically has a positive cosmological constant. BrentUnfortunately, my understanding of the scale factor and cosmological constant as they relate to the various geometries is insufficient to appreciate your comments. Maybe you could restate your above comments with that in mind. TIA.
Didn't you read Vic's "Comprehensible Cosmos"? Why are you over here on the everythinglist asking physics questions anyway, Alan? You should try the stackechange or quora.
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