# Geometry of the universe

1. Jun 17, 2014

### elusiveshame

I know there's no definitive answer to this, and there's a few different models that give different explanations on why they're using a flat model, or a curved model, but my question is why wouldn't the geometric shape of the universe be spherical or a hyperbolic sphere since everything else is in the form of a sphere/spheroid shapes and most objects follow an ecliptic orbit, or am I thinking too simplistic / narrow sighted?

2. Jun 17, 2014

### Staff: Mentor

"Everything else" is acting under the influence of a three-dimensional central inverse-square gravitational force - that's why orbits about the sun are elliptical and why large enough masses such as the planets settle into spherical shapes. The universe occupies a four-dimensional spacetime and there's no central point to do the $Gm_1_m_2/r^2$ thing with... so the comparison doesn't apply.

Last edited: Jun 17, 2014
3. Jun 17, 2014

### Matterwave

It sounds like your statement is analogous to "the objects on my table take a spherical shape, therefore my table is spherical".

The spatial shape of the universe, assuming it is isotropic and homogeneous, can be one of 3 possibilities depending on the spatial curvature (which must be spatially constant since the universe is isotropic and homogeneous). If the spatial curvature is positive, the universe will have a spherical shape (a 3-sphere), if the spatial curvature is 0 the universe will be flat, and if the spatial curvature is negative the universe will have a hyperbolic shape (like a 3-D saddle).

Remember though that these are the "shapes" of a 3-D object embedded in a 4-D manifold. It's not the usual 2-D visualizations that you are used to. A 3-sphere is different than the regular 2-sphere we are used to.

Also what is a hyperbolic sphere? I have never heard of such a term.

4. Jun 17, 2014

### elusiveshame

Hm. So if I understand you correctly, objects, such as planets and stars occupy one model that is separate from the universe, but is inside the universe, just at a local level (galaxies, for example) with different governing laws, or am I off base here?

I'm very new to this subject, so please forgive my ignorance.

Edited to add: by hyperbolic sphere, I meant a like a sphere with an indent like saddle. I think I'm way over my head at this point haha.

5. Jun 17, 2014

### Matterwave

The laws governing the universe are assumed to be the same everywhere. The model we use for gravitation is general relativity. This model applies to stars, to galaxies, as well as to the universe as a whole. But just because my cellphone follows the same laws of physics as a rubber ball doesn't mean they have to be the same shape...where would one draw this conclusion?

A "hyperbolic sphere" is not a standard terminology. And I don't really know what you mean by it. Maybe you mean a hyperbolic geometry: http://en.wikipedia.org/wiki/Hyperbolic_geometry

6. Jun 17, 2014

### micromass

Maybe he means the psuedosphere?

7. Jun 17, 2014

### elusiveshame

I think I may have worded my question in convoluted way, or maybe left out some details of what I was asking.

I didn't necessarily mean a sphere, it could be an oblong curved cylinder, or any shape with curvature to the edges.

I was/am under the impression that dark energy is causing the expansion, but would I be incorrect to think that dark energy would also aid in the creation of stars which then create it's gravitational forces to create galaxies and solar systems?

That's why it's hard for me to imagine a "flat" universe, or a universe with a formal shape/design as it seems that everything is uniform (stars are spherical, planets, comets, asteroids are spherical, they all revolve on an ecliptic plane, and so on.

I will definitely check out the Michelson-Morely type experiments and maybe that will help clear up some confusion.

8. Jun 17, 2014

### Staff: Mentor

The MM experiments are good stuff, and essential to the development of Special Relativity, but don't expect them to help with your question - the connection is somewhere between tenuous and non-existent.

9. Jun 17, 2014

### Staff: Mentor

If it was my post that you're replying to, no, you're not understanding me correctly... But then again I could have been more clear... Sorry about that, and let me try again.

The governing laws are the same everywhere (as far as we know - there's no evidence otherwise), but the same laws will produce different results in different situations. The planets assume a spherical shape because the gravitational attraction within a planet-sized lump of reasonably dense matter will pull it into a sphere; the planets travel in elliptical orbits around the sun because the gravitational attraction between two widely separated massive bodies pulls them into such an orbit. Same law of gravity, same physics, different configuration of matter for gravity to work on, you get different results.

The same laws are at work on the universe as a whole, but because the universe is neither a planet-sized lump of reasonably dense matter nor two widely separated massive bodies so there's no particular reason to expect to get a sphere or an ellipse as the result.