Wright's 'best fit' universe does not expand out into empty space

1. Jul 22, 2007

marcus

Ned Wright's best fit standard LCDM is simply one possible concrete version of the usual LCDM model that cosmologists use. It has the normally preferred parameters (0.27, 0.73, 71) plus the estimate that Wright gave of Omega = 1.011.

That's what he gave in January 2007 as the best LCDM fit to some 4 or 5 independent sets of data---currently the best and most complete he could get his hands on.

IMHO the value of having a CONCRETE instance of the standard model is pedagogical. It gives people something definite to think about. So I want to try it out pedagogically.

I will use the 'best fit' universe model in conjuntion with Wright's cosmology calculator---including this new version
http://www.astro.ucla.edu/~wright/DlttCalc.html
this version has the normal parameters (0.27, 0.73, 71) as default values so you don't have to type them in, and it converts light travel time to redshift z.

there is an arbitrary cutoff at 13.666 billion years, at which time the redshift is 999,999,999. that is, according to the calculator, distances have expanded
a BILLION-fold in the past 13.666 billion years.

it is already very crude and naive to be pushing a calculator that far back, and it is good he makes that artificial cut-off because it certainly would not do to try to push it back any farther----but for the sake of concreteness I will use the calculator's numbers back that far.

Last edited: Jul 22, 2007
2. Jul 22, 2007

marcus

the inspiration for this thread

this thread was inspired by a conversation in the Astrophysics forum where someone pictured the universe as a 3D ball of stars expanding out into empty space.

a lot of people fall prey to this erroneous mental image---and most, I think, could not say what popularization book or media piece gave them this idea.
If anyone knows of a book by a reputable author that actually says this, please let us know. Such books should be burned, or at least people should be warned about them.

this misconception was very well disposed of by Lineweaver Davis article in the March 2005 Scientific American which is ON LINE. It is free to download, very clearly and simply written, and it completely demolishes the idea that the universe is a 3D ball of stars expanding into empty space. PF mentors and others have repeatedly given the link and encouraged people to read it. But many people have not read, or have not assimilated, this or any similar article.

I now suspect the reason that the Lineweaver Davis article, and things like it, have not had the expected effect is because people do not have a clear definite consistent picture to put in the place of the mistaken one.

Without a concrete replacement picture, it is useless to argue. No matter how many times you eject it, the mistaken picture will keep creeping back in to fill the conceptual void.

Last edited: Jul 22, 2007
3. Jul 22, 2007

marcus

dimensions of space today

If you take Omega = 1.011 and the usual figure of 71 for the current Hubble parameter, you get a space that is determined by those measurements. Those characteristics essentially determine space to be a THREE-SPHERE with radius of curvature 130 billion LY.

Since some people have trouble imagining a three-sphere, we need to be extra clear. I'll try to distinguish explicitly between the (solid volume) BALL and the surface of a ball which I will call a SPHERE. Intuitively, the sphere is the hollow thing and the ball is the solid thing.

A sphere of any dimension can exist as a topological space on its own without any space of higher dimension surrounding it or inside it.
And in particular, the 3D sphere, or three-sphere, which can be imagined in one way as the surface of a 4D ball, can also exist in its own right without any 4D ball inside it and without any 4D space surrounding it.

One way to teach yourself to picture a three-sphere is to think about lower-dimensional analogs for a while and what it would be like to be a linear being living in a ring, or to be a flat being living in a two-sphere (the familiar surface of a 3D ball)
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IF today's space has radius of curvature equal 130 billion lightyears, then since, according to Wright's calculator, 13.666 billion years ago SPACE WAS A BILLION TIMES SMALLER, it must have had a radius of curvature equal to 130 lightyears.

It is easy to see that. just go to the calculator
http://www.astro.ucla.edu/~wright/DlttCalc.html
and over on the left put in 13.666 for the travel time in billions of years
and press the "general" button, or the "flat" button will do equally well
And the calculator tells you a redshift z = 999,999,999, which means a billion-fold expansion. So. that's it.

Let's think about that small hot universe 13.666 billion years in the past. It has a circumference, or great circle tour, of 800 lightyears---just multiply the 130 lightyear figure by 2pi. Since it is a billion times smaller, it must be a billion times hotter---3 billion degrees Kelvin. Since its linear dimension is smaller by a factor of 10^9, its density must be greater by a factor of billion-billion-billion, or 10^27.

I'm being sloppy about the calculation but it gives the basic idea.
Maybe one of the cosmology grad students who hang out here would like to add some discussion and detail. I have to be off the computer for a while and take care of some other things. Let me know if anyone sees really major errors.

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somebody might be wondering what is the radius of curvature. If the sphere is embedded in some higher-dim. space then it is just the ordinary radius. I only say radius of CURVATURE because i don't want to assume that our space is embedded in some higher-dim space.
the radius of curvature is something a creature can measure FROM WITHIN just by moving around.
like a 2D flat being living in a 2-sphere could make triangles and measure interior angles and he could discover the radius of curvature of his world that way (but he might have no concept of a spatial third dimension). He does it all from within 2D space, he doesnt have to get outside. So the radius of curvature is the radius that you measure by moving around in your world and discovering its curvature, like by measuringing interior angles of triangles. If they dont add up to exactly 180, then you know your world is curved.
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somebody might be wondering about the VOLUME of our space------this is analogous to the area in the two-sphere.

in the case of a threesphere the formula is 2 pi R3
where R is the radius (of curvature :-))

Last edited: Jul 23, 2007
4. Jul 24, 2007

marcus

Uh oh! Typo.
too much in a hurry, left out the exponent on the pi. Should be pi-square

the 3D volume of a threesphere formula is 2 pi2 r3
where r is the radius (of curvature)

a nice way to remember is that 2 pi2 is about equal to TWENTY
so to find the volume you just cube the radius and multiply by twenty.

Last edited: Jul 24, 2007