Non-zero curvature

[sanctus]

Hello all,

I was just wondering how a non-zero curvature of the universe could be explained intuitively, because my following reasoning does not really allow it, while there are plenty of models where you consider that we could live in a non-flat universe.

I start from the consideration that if space-time is curved somewhere then it is this due to a mass somewhere nearby. Now, if one considers a Fridmann-Lemaitre background universe with some perturbation to it, one is saying that there is a (spatially) homogeneous and isotropic universe with a small perturbation to it. Since the perturbation is small, there cannot be a point in the universe where there is a bigger concentration of mass, so nothing to give an overall curvature to the universe.

Ok, if you suppose the universe such that the points in space-time where mass is have a finite volume, but allow space-time to go further out (what seems a bit strange to me, but anyway how do you define space-time?) then the curvature can be there because the mass inside bends space-time compared to the space-time outside the mass concentration...but this a bit fishy reasoning to me, seeming only to work if the curvature is such that the universe is closed (but then how can you have a space-time outside the mass concentration in a closed universe?).

Hope you got my point, in other words I am looking for an intuitive reason on how and why the universe could have an overall curvature?

[freeztar]

Have you read the thread "What is spacetime?" ?
We are currently trying to determine this in a philosophic manner.

Originally Posted by sanctus

how can you have a space-time outside the mass concentration in a closed universe?

Indeed.
Physically, there seems to be only three possibilities:
1) Space itself has an apparent property that causes curvature or
2) Curvature of space is only possible within the vicinities of massive objects
3) Curvature is non-existant

We can rule out number three because of gravity. Number two is much more difficult to rule out, while number one is uncomfortable philosophically.

I'm unaware of studies regarding "voids" in space. Most studies are performed on luminous objects, things with substance (mass). If anyone is aware of studies regarding "voids", I'd be very interested to know more about it!

[Erasmus00]

Originally Posted by sanctus

Hope you got my point, in other words I am looking for an intuitive reason on how and why the universe could have an overall curvature?

The answer is that to a first approximation in Friedman type universes, we think of the universe as full of a perfect fluid. This means that (on large scales) we think of the universe as full of stuff.

If the stuff is very dense, the gravitational pull should try to bring the universe back on itself, resulting in a positive curvature everywhere (like a sphere).

If the stuff is under dense, gravity cannot pull the universe back on itself, and we end up with either a hyperbolic universe (negative curvature everywhere) or flat. The flat case is balanced on the edge of a knife, however, only one density allows for 0 curvature.