When talking cosmology what exactly is a manifold, is there any

[wolram]

When talking cosmology what exactly is a manifold, is there any observational evidence that we live in one ?

 

[jedishrfu]

in general a manifold is an n-dinensional space:

http://en.wikipedia.org/wiki/Manifold

there's been some discussion that we live in a holographic universe or that we are part of a multi-verse ie many universes based on the many worlds interpretation of QM, no proof but interesting discussions. these both require n-dimensional manifolds beyond our current spacetime view.

 

[wolram]

From wiki, http://en.wikipedia.org/wiki/Shape_of_the_Universe.

For a flat spatial geometry, the scale of any properties of the topology is arbitrary and may or may not be directly detectable. For spherical and hyperbolic spatial geometries, the curvature gives a scale (either by using the radius of curvature or its inverse), a fact noted by Carl Friedrich Gauss in an 1824 letter to Franz Taurinus.[6]
The probability of detection of the topology by direct observation depends on the spatial curvature: a small curvature of the local geometry, with a corresponding radius of curvature greater than the observable horizon, makes the topology difficult or impossible to detect if the curvature is hyperbolic. A spherical geometry with a small curvature (large radius of curvature) does not make detection difficult.
Analysis of data from WMAP implies that on the scale to the surface of last scattering, the density parameter of the Universe is within about 0.5% of the value representing spatial flatness.

So the most preferred model a flat topology would be undetectable ?

 

[Nabeshin]

When talking cosmology what exactly is a manifold, is there any observational evidence that we live in one ?

I think this question is fundamentally backwards. A manifold is something we have created in our minds, while (I think most would agree), the universe really exists. It is rather that a manifold seems to well represent the space we live in.

 

[bcrowell]

When talking cosmology what exactly is a manifold, is there any observational evidence that we live in one ?

If it's not a manifold, then what is the alternative? For example, a manifold with boundary is not a manifold -- is that the kind of thing you have in mind? The evidence that it's not a manifold with boundary is that we have observed lots of places in the universe, and none of them look like boundaries.

Another possibility would be that it's not a manifold because some regions have 4 dimensions, and other regions have some other number of dimensions. The definition of a manifold requires that the space have the same dimensionality everywhere. Again, the evidence would be that we don't observe any regions of the universe that seem to have the wrong number of dimensions.

I don't understand how your #3 relates to this question at all.

 

[Chalnoth]

In General Relativity, the mathematical object which describes the space-time is a manifold. Our experimental measurements of General Relativity show that GR is an extremely accurate description of how the universe behaves.

Now, is our universe really the idealized mathematical object of a manifold? Well, my guess is probably not, because General Relativity is probably not entirely accurate, particularly at very short distances. It is, however, clearly an extremely good approximation.