# Assumption of spherical nature of the universe

1. Jul 5, 2009

### Rymer

I guess the question is: Is the often used spherical symmetry of the universe just an assumption or is there evidence to support this?

I don't mean, nature of 'observing' so much has the properties or symmetry?

Trying for an example: many particles have spin -- does the universe have 'spin'? And if so, is this spin a spherical symmetry? ... or cylindrical? or something else?

2. Jul 6, 2009

### Chronos

The universe appears spherical to all observers no matter where or when they exist. that does not mean it is 'truly' spherical, or of any other particular shape.

3. Jul 6, 2009

### Rymer

Any way to tell? Some measurable property -- spin, expansion difference?

4. Jul 6, 2009

### marcus

Curvature is the measurable property, taken together with the usual uniformity assumptions made in cosmo.
Largescale homogeneity and isotropy.

So if you measure a positive curvature around us, out as far as we can see, and you assume that we are not special and the rest is roughly similar in largescale average density, curvature etc. Then you get a hypersphere.

Look in Table 2 on page 4.

They give an errorbar on the curvature. And they can't say if it is positive or zero or maybe even slightly negative. But a piece of the 95% confidence interval is in positive territory. So they consider that case what if it is true? And they calculate [a lower bound on] the RADIUS of the hypersphere, that you would have if the curvature were at the upper end of the 95% confidence range. they call it "radius of curvature" and [the lower bound] comes to around 100 billion lightyears.

So the key thing to observe and measure is the largescale curvature. You do that by counting the galaxies at various distances, and by statistical study of the Background temperature map. Then you translate the curvature you measure into a "radius of curvature".

So far no conclusions. But a new spacecraft called Planck was launched this year in May and is out at Lagrange Two now, observing the microwave Background. The data from Planck will almost certainly narrow down the errorbar on the overall curvature measurement. Give it three years, I would guess. Then we will reconsider the possible "hypersphere nature" of the universe

If you want help finding the Komatsu paper and interpreting Table 2, let us know. Keep asking questions like this, they are fun for everybody!

Last edited: Jul 6, 2009
5. Jul 6, 2009

### Rymer

Thanks!

Yes, I would like to attempt to read the Komatsu paper.

6. Jul 6, 2009

### TalonD

"radius of curvature" and it comes to around 100 billion lightyears.

So that would be the minimum then and not the maximum?
because the margin of error means it has to be at least that big and not smaller, but it could be bigger?

7. Jul 6, 2009

### marcus

Talon, thanks so much for catching that! The maximum curvature corresponds to the minimum possible radius of curvature. What they gave was a LOWER BOUND on the RoC. The radius has to be at least that 100 billion lightyear. And it could be infinite (infinite radius corresponds to flat case). I was in a hurry and forgot to say.

I went back and edited my post in bold red, to make sure this is clearly understood.

8. Jul 6, 2009

### Rymer

I'm apologizing ahead of time for this question. I'm not that good a visualizing more than 3 dimensions.

The universe has been often described as a 'hypersphere'. I gather this is due to the points you have made above. But could the same be argued for a 'hypercylinder'?

It seems that a spherical assumption is putting constraints on the 'time' coordinate -- not sure???

If so, does it really change anything???

9. Jul 6, 2009

### marcus

That is a strong ambition. I can help with a few parts, like Table 2. The whole paper is too long and technical. But even trying to understand bits and pieces can be a chance to learn. So in case anybody else wants the link http://arxiv.org/abs/0803.0547

The paper is interpreting the cosmology implications of the first 5 years of WMAP data. There were some 6 or 8 WMAP5 papers that came out at the same time in 2008. This one is the most highly cited because cosmology is of intense interest. The author list is like a who's-who of worldclass cosmologists. Ned Wright, David Spergel, Joanna Dunkley, Lyman Page. I didn't know of Komatsu, but their making him lead author this time puts him on the map for me.
WMAP is Nasa's biggest single purpose astro project. The HST is wonderful but it is very multipurpose, many creative applications. they think up stuff to do and apply for a timeslice. WMAP is for one thing: to map the cosmic microwave background in high detail and to deduce everything about the universe that you can from that map.

The Komatsu paper derived two sets of results about the universe, one set was what you could deduce just from their own WMAP observations, the other set of numbers is what they call "WMAP+BAO+SN". That means they combined their own data with two other sets of data collected by the Hubble Space Telescope and other instruments. SN is supernova data and BAO is galaxy counts, made at different distances or redshifts, in order to find waves of density or "acoustic oscillations" in the distribution of matter. BAO stands for "baryon acoustic oscillation". So you look out and you count the number of galaxies in a certain distance shell, like from redshift 1 to redshift 1.5, and then you count the number in the next shell from z = 1.5 to z = 2.0. I am oversimplifying to a shameless degree but just want to give the idea that when you see a two columns of numbers, one labeled WMAP and one labeled
WMAP+BAO+SN, then you should pay attention to the second column because it is based on broader data.

As a newcomer you would be doing very very good if you could just understand a few things from their Table 2, the column labeled broad base data (from three major studies instead of just one.)

I should have made that clear. A hypersphere comes up when one is modeling space. Forgetting about time. The time coordinate is nowhere in the picture so it is not constrained by the picture. Some people play it fast and loose and imagine the radius of curvature as time itself. Geometrically the radius of curvature is currently increasing at a rate of 1/130 to 1/140 of a percent every million years. It increases at the same percentage rate that distances within the hypersphere increase.

It's like they think of space as the surface of a balloon (2D) and they think of time as the radius of the balloon. And then they go one dimension up and the hypersphere (3D) is the surface of a 4D ball and increasing time is the increasing radius of the ball. (which is what we call the RoC of the hypersphere.
Personally that makes me nervous. Because in the history of the universe the RoC has increased at very different rates so making it correspond to some realistic clock time seems to me impossible or more trouble than it is worth.

I would rather just call the hypersphere S3 (standard math symbol for the "threesphere") and take a cartesian product
S3 x R of the hypersphere with the real line, with the real line serving as time axis. Maybe that is the cylinder you were talking about.

Do you know the deSitter universe? A kind of coke-bottle cylinder, with a very narrow waist where a kind of bounce happens? That is topologically the same as S3 x R. It's not a bad picture. You could easily do worse. Or two cones joined point to point.

Anyway what I meant was the universe could be spatially S3.
Spatially a hypersphere. No intention of constraining the time axis.
When they measure the curvature they measure it as it presumably is at this present moment.

Last edited: Jul 6, 2009