On 11/10/2017 1:01 PM, agrayson2...@gmail.com 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 <javascript:>> 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 <javascript:>> wrote:
On 11/9/2017 8:55 PM, agrays...@gmail.com <javascript:>
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.
Brent
TIA.
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