# Shape of the Universe

## Main Question or Discussion Point

How is it not possible that the universe is shaped like a sphere?

What evidence do we have that shows it is expanding in a single drection or some variation that of?

I recently heard that the origonal spherical theory doesn't work because of the increased speed of expansion, what I want to know is, how?

George Jones
Staff Emeritus
Gold Member
I just found out about this work (Campanelli, Cea, Tedesco, Physical Review Letters, 29 September 2006), http://www.arxiv.org/abs/astro-ph/0606266" [Broken], last night, and I haven't had chance to read it yet.

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If your talking about the shape of space then the following stuff is relevent, if not ignore :)

Basically there are three possibilites. One, the universe is Euclidian, that is it is flat, the angles in a triangle add up to 180 degrees and pi is what we know it to be etc. The other two are positive and negative curviture. Picture a cloth (consider the lilly!). If you take each point on the cloth and add more material, you will get positive curviture. Its kind of hard to visualise without an actual cloth but anyway, its the idea that the universe curves off into infinity.

With negative curviture however you get the opposite, you get bits of material removed and so it curves the other way. This results in the possibility of a closed sphereical universe ie the universe is cyclical and you can go round the entire 'circumfrance' and get back to where you started (keeping in mind this is a 2d representation of 4d spacetime)

Now according to the CMB (cosmic microwave background) the universe is flat. This is because we know what it should look like if the universe is flat, and when we measure it we get the same thing. i did have some diagrams that explained this but i lost them :( basically if you get some kind of curviture you get parts of the CMB looking bigger or smaller than they actually are, kinda like gravitational lensing but without gravity as the cause (although gravity warps spacetime in a similar manner)

hope this helps!

Garth
Gold Member
FunkyDwarf said:
Now according to the CMB (cosmic microwave background) the universe is flat.
Actually the CMB data is consistent with a universe that it is conformally flat - but nobody else acknowledges this. :uhh:

A linearly expanding or “Freely Coasting” model that is also spatially spherical (k = +1) would be conformally flat.

Garth

im not sure i understand what you mean by conformly flat, are you saying as oppose to having lumps in it?

also i should point out (shoulda said so in original post but anyway) i think this kind of measurement is flawed because you are measuing something you are immersed in. Its like a fish in water saying water doesnt refract light because he sees it going straight (bad example but anyway) in the same way we are in a universe that we would perceive as flat even if by some outside observer is considered curved because we are in it and doing measurements in it

Garth
Gold Member
First, a fish can observe the refraction of light underwater, if it was clever enough, most easily in the phenomenon of total internal reflection, but also if it had the correct apparatus, it could observe refraction in an experiment to determine the path of light through water of changing temperature, pressure and density.

This is just what cosmologists try to do in observing the universe, because it is possible to test its intrinsic geometry to see whether it is Euclidean or not. The WMAP data set is just one, and a very good, way of doing this.

Conformally flat means the geometry of space is Euclidean even though the global geometry may not be. An example of this would be a sheet of paper curved into a cylinder or fashioned into a cone. Geometry drawn on the 2D surface of the paper would still be Euclidean, the internal angles of a triangle would still sum to 1800 etc., but the surface would not be infinite in the direction orthogonal to the axis, even though it is unbounded.

The intrinsic geometry of the 'surface' being considered is described mathematically by its metric tensor. Conformal transformations transform this metric in such a way that the angles between points on the surface are preserved. As WMAP measures angles between the anisotropies in the CMB a statement that the WMAP data set is consistent with a model of a spatially flat universe implies that it also consistent with a surface that is a conformal transformation of such a model.

Garth

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yeh i said the fish was a bad example :P

marcus
Gold Member
Dearly Missed
George Jones said:
I just found out about this work (Campanelli, Cea, Tedesco, Physical Review Letters, 29 September 2006), http://www.arxiv.org/abs/astro-ph/0606266" [Broken], last night, and I haven't had chance to read it yet.
Physics News Update has an item about the Campanelli et al paper

does anyone want to explain a little? George? ST?

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Garth
Gold Member
If the Surface of Last Scattering is ellipsoidal rather than strictly spherical, with a small eccentricity of about 10-2, then this would affect the quadrupole signal to the CMB anisotropy power spectrum and it could result in a drastic reduction in the quadrupole anisotropy without affecting the higher multipoles.

A neat idea, that does depend of course on the quadrupole signal actually being deficient, however the low-l power spectrum may be affected at the octupole signal as well and these deviations from gaussality (randomness) appear to be also aligned with local geometry. (The axis of evil)

They may just be explaining one possible problem by introducing another......

Garth

marcus
Gold Member
Dearly Missed
Garth said:
If the Surface of Last Scattering is ellipsoidal rather than strictly spherical,
Hi Garth, I saw their figure showing an ellipsoidal surface of last scattering. What I do not understand at the moment is how one can have an ellipsoidal SoLS.

they say that a weak magnetic field throughout the relevant portion of space could be one thing that might cause this eccentricity---would you like to say in elementary fashion how a magnetic field would do that?

Garth
Gold Member
I will just have to accept their word for it!

The magnetic field enters into the pressure term of the field equation and affect the rate of expansion anisotropically. Hence the distance from the SLS to the observer varies depending on the direction.

Garth

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George Jones
Staff Emeritus
Gold Member
marcus said:
does anyone want to explain a little?

What I do not understand at the moment is how one can have an ellipsoidal SoLS.

they say that a weak magnetic field throughout the relevant portion of space could be one thing that might cause this eccentricity---would you like to say in elementary fashion how a magnetic field would do that?
Let me see if I can write something that complements what Garth wrote.

Friedmann-Robertson-Walker models of the universe assume spatial homogeneity and isotropy. I guess they are popular for a number of reasons: they exhibit a sort of Copernican cosmological principle; the symmetries make them easy to analyze; they model observations fairly well.

But nowhere is it written in stone that the universe has to be so simple.

This paper models an ansitropic universe that has two scale factors, a and b, and that has spacetime metric

$$ds^2 = dt^2 - a^2 \left( t \right) \left( dx^2 + dy^2 \right) -b^2 \left( t \right) dz^2.$$

Energy-monemtum tensors that give rise to this solution to Einstein's equation have an an isotropic part, from stuff like dark energy and normal matter (galaxies), and an anisotropic part. Uniform magnetic fields can give rise to suitable anistropic energy-momentum tensors.

The paper assumes that at the present instant in cosmic time, a and b are equal, so that the spatial geometry is presently spherical. If the scale factors evolved at different rates, then in the past, in particular at the time of last scattering, a and b were different, and the spatial geometry of the universe was ellipsoidal.

The paper also looks at the physical reasonableness of a magnetic field that does the job. The paper says that if the magnitude of the magnetic field evolves in time as the inverse of the square of the scale factors, then, to within an order of magnitude, the cosmic magnetic field presently observed seems to be appropriate.

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marcus