On Friday, November 8, 2019 at 4:47:15 PM UTC-6, Alan Grayson wrote:
> https://gizmodo.com/a-round-universe-would-be-bad-news-for-physicists-1839647806
> Personally, FWIW, I don't believe the universe is open. When physicists 
> claim it is "flat", they must mean "asymptotically flat", leaving the 
> possibility of really being closed. AG

The Friedmann-LeMaitre-Robertson-Walker (FLRW) metric

ds^2 = dt^2 - (1 - kr^2)^{-1}[dr^2 - r^2(dθ^2 + sin^2θdφ^2)]

is flat for k = 0 and a sphere for k = 1. For k = -1 it is a hyperbolic 
surface. I wrote on how the FLRW dynamics can be found with just Newtonian 
mechanics and gravity on Stack exchange 
 The dynamical equation is found from the energy E_{tot} = 0 constraint

0 = (a'/a)^2 - 8πGρ/3c^2 + k/a^2,

where a is the scale factor for expansion or contraction of space and ρ the 
density of the vacuum energy. For k not zero there is in addition to this 
dynamical equation a term -k/a^2, where a is the scale parameter, or 
related to the radius, of the spatial surface. For an expanding space this 
term clearly becomes very small. 

If the universe is a sphere and not flat it blows away a theory I worked 
last decade on how a quantum critical point in inflationary physics. 
However, it does gives support to a hypothesis I have that the pocket world 
generated in the unstable vacuum of the inflating de Sitter manifold 
"bubbles off" that manifold as a closed spatial surface. These pocket 
worlds are regions where the high energy, so called false vacuum, of this 
inflationary de Sitter manifold decays or transitions into a low energy 
vacuum. See diagram below. Here the right side is stretched out to 
illustrate there is a time delay for the transition as a "slow roll." If 
this remains a pocket, similar to a bubble in Swiss cheese, there is then a 
boundary. This boundary has some ugly features to it. However, this 
boundary will have quantum field content to it, and this may then 
transition into topological quantum numbers for a closed sphere. It is 
again a type of quantum critical point.

I will say I am withholding judgment on this. The problem I see is that 
with inflation and the general "flattening" that occurs with that this 
deviation from flat to spheroidal geometry would be small. I estimate the 
distance to the edge of the bubble or pocket world is around 2 trillion 
light years, which would be observed here as highly red shifted quantum 
gravitational data. If this region at the end of inflation by a phase 
transition transformed the boundary information into topological numbers 
for a sphere, or an spherical orbifold, this 3-dimensional sphere would now 
be around 159 billion light years in radius. The volume of this 3-sphere 
would be V = (8π/3)r^3 ~ 4x10^{24}ly^3 and the volume of the region we can 
observe to the CMB is about 45billion light years out or 9x10^{22}ly^3 and 
so angle deviations would be around .02rad (1.3 degrees). A telescope 
looking at some region of the CMB would see a slight excess of 
magnification. This is not impossible to detect, but given the state of the 
art it is still tough. Also since Planck and the WMAP before it integrated 
data this would tend to be somewhat integrated out.  


[image: inflaton potential.jpg]

You received this message because you are subscribed to the Google Groups 
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email 
to everything-list+unsubscr...@googlegroups.com.
To view this discussion on the web visit 

Reply via email to