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

1. Jan 25, 2007

### 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.

2. Jan 25, 2007

### 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: