Best fit three-sphere radius 130 gly (after Ned Wright)

[marcus]

In his most recent, Ned Wright gives the best fit Omega as 1.011.

He hastens to say that since the fit is not all that better than for Omega exactly 1, space being flat infinite, one cannot rightfully conclude that Omega > 1.

However suppose, simply as an intellectual exercise, that one were to take this best fit Omega literally on its own terms. Imagine that the U really is as Wright has determined.

Then we imagine space as a bumpy dimply THREE-SPHERE, and the radius of curvature, or the actual fourspace RADIUS if you like to picture the threesphere living in a boyscout Euclid fourspace, is 130 BILLION LIGHT YEARS.

Try it on, and if you like the fit, wear it.

 

[marcus]

The formula in George Smoot's lecture notes

George Smoot has sometimes taught Physics 139 at Berkeley, an advance undergrad course in Spesh-and-Gen Relativity with supplemental Cosmology.
You can get his notes if you google "smoot notes geometry universe"

The notes give a simple formula for the radius of curvature. It is incredibly simple but let's try it. At least this will give a first approximation.

You just take the HUBBLE LENGTH which we usually say is 13.8 gly, and you divide it by a factor which is sqrt(Omega - 1). that is all.

If we use the best fit Omega of 1.011, then Omega - 1 is 0.011
and the square root is 0.105

and if you divide 13.8 billion lightyears by 0.105 you get

130 BILLION LIGHT YEARS.

So if we live in a threesphere, and you want to picture it contained in boyscout fourspace, and as having a radius, this is a possible guess about the radius.

If I have made a mistake in reading Smoot's notes or in calculating please let me know

The Ned Wright paper that I am having fun with is mentioned here:
https://www.physicsforums.com/showthread.php?p=1220828#post1220828

New Wright's new paper
just came out
http://arxiv.org/abs/astro-ph/0701584
discussion section page 14:

"Using all the data together
gives the plot shown in Figure 5. The best fit model is slightly closed with
Omega_tot = 1.011 and M = 0.315. "

Wright is an WMAP princ. investigator.

Here is Wright's paper

Constraints on Dark Energy from Supernovae, Gamma Ray Bursts, Acoustic Oscillations, Nucleosynthesis and Large Scale Structure and the Hubble constant
Edward L. Wright (UCLA)
16 pages, 8 figure

"The luminosity distance vs. redshift law is now measured using supernovae and gamma ray bursts, and the angular size distance is measured at the surface of last scattering by the CMB and at z = 0.35 by baryon acoustic oscillations. In this paper this data is fit to models for the equation of state with w = -1, w = const, and w(z) = w_0+w_a(1-a). The last model is poorly constrained by the distance data, leading to unphysical solutions where the dark energy dominates at early times unless the large scale structure and acoustic scale constraints are modified to allow for early time dark energy effects. A flat LambdaCDM model is consistent with all the data."

the initial announcement of WMAP3 "implications for cosmology" paper by Spergel et al already contained hint of this.
warning: it doesn't prove anything. the INFINITE FLAT universe is still consistent, it just is not the best fit. the best fit is with nearly spatially flat, slight positive spatial curvature and therefore the best fit is spatially finite.

flat would be Omega = 1.00 exactly, the best fit is Omega = 1.011

However as Ned Wright is careful to say: a flat model is "consistent" with the data