Curvature of universe

[NaxAlpha]

The curvature of universe is -ve or +ve

How to determine it?

[elfmotat]

In cosmological models of the universe in General Relativity, for example the FLRW metric, positive "overall" curvature refers to spherical geometry and negative curvature refers to hyperbolic geometry. In a spherical universe, the angles in all triangles add up to greater than 180°. In a hyperbolic universe, the angles in a triangle add up to less than 180°. A flat universe's triangles have angles that add up to exactly 180°. So a way to figure out the "shape" of the universe would be to measure the angles in triangles. We've conducted such experiments, and so far we find that the universe is approximately flat. If the universe does have some curvature to it, it's too small to detect with current methods.

[NaxAlpha]

I think we should see in another view

Drawing a triangle on a flat paper

We rotate this paper in 3rd dimension to make curvature

As we determine 2D curvature by rotating plane in 3rd dimension

So if we want to determine curvature of universe we should see in 4th dimension

But I don't know weather the fourth dimension is time or length

If 4th dimension is time then according to Einstein's time delay formula universe should be +ve curvature

If 4th dimension is also a dimension of length then according to lorentz contraction formula universe should be -ve curvatured

I've to know about it!

[elfmotat]

Drawing a triangle on a flat paper

We rotate this paper in 3rd dimension to make curvature

As we determine 2D curvature by rotating plane in 3rd dimension

 

This simply isn't true. A cone is still "flat" because you can unfold it and it will lie flat on a table with no bumps. If you draw a triangle on a cone, its angles will add up to 180°. A sphere, on the other hand, has "intrinsic curvature." No matter how hard you try, you won't be able to make an unfolded sphere lie flat on a table.

 

The curvature of General Relativity is intrinsic curvature. Spacetime doesn't need to be embedded in an extradimensional space for there to be curvature.

Edited January 12, 2013 by elfmotat