geometry

[Speculatrix]

I have a question. I'm not even sure that it makes sense or is a worthy question, so please bear with me.

Is there a geometry written for the current (accepted) view of the universe? It seems there must be a geometry that deals with curved space and other such features, but I have never heard of one. For a while people were just sort-of writing geometries--just making up systems that worked whether they had been seen or not, right? It seems crazy that someone could (or would) write one that worked for our universe without knowing its details. Did someone construct one to the universe in modern times? Or have we just never needed a complete geometry? It seems we must be using some geometry, but I don't know what it is.

Thanks for any insight. (I realize my question was probably worded badly and therefore partially incoherent.)

-Speculatrix

[LURCH]

There are several, we don't jknow which is correct, but this recent model (http://www.space.com/scienceastronomy/universe_soccer_031008.html) seems to show a lot of promise.

[Ambitwistor]

People usually start by assuming that space is homogeneous and isotropic (i.e., its geometry looks the same at all places and in all directions). Of course this is not exactly true, but this "cosmological principle" has been borne out by observations as pertaining the average, large-scale structure of the universe. This greatly restricts the possible spatial geometries. When you apply Einstein's field equation to determine how the geometry will change with time, general relativity restricts the possible spacetime geometries even further. You end up with the Friedmann-LeMaitre-Robertson-Walker (FLRW) cosmologies. Observations tell us that space is very close to being universally flat, so people usually use a flat FLRW model, although you can also use a non-flat one if you make the curvature sufficiently small.