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
Brent
On Thu, Nov 9, 2017 at 4:42 PM, Brent Meeker <[email protected]
<mailto:[email protected]>> wrote:
Cosmologist think the universe is spatially flat. That just means
triangles have interior angles summing to 180deg. It doesn't have
anything to do with extent. But the universe is not flat in
spacetime; it's expanding and at an increasing rate.
Brent
On 11/9/2017 3:10 PM, [email protected]
<mailto:[email protected]> wrote:
IIUC, the difference is huge. In the former case, the universe is
open, spatially infinite with infinite mass (assuming a nonzero
mass distribution on large scale everywhere), whereas the latter
is closed, finite in spatial extent and mass. But I notice that
most cosmologists claim the universe is *flat*, as in
mathematically flat. Are they just speaking loosely and really
mean the universe is ASYMPTOTICALLY flat? I find it contradictory
for a universe which is finite in age, to be truly mathematically
FLAT. TIA.
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