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We need to distinguish between the curvature of a specific location versus the curvature of the universe as a whole. As I understand it, for a universe that's
by lutusp 13y ago
We need to distinguish between the curvature of a specific location versus the curvature of the universe as a whole.
As I understand it, for a universe that's being uniformly accelerated, by for example dark energy, its overall curvature should be negative. In the absence of dark energy, and for a universe whose masses possess escape velocity (no more and no less), the classic zero-energy assumption of modern Big Bang models, the overall curvature is zero (i.e. flat). For a universe that has less than escape velocity and will recollapse, an idea that has now been pretty much abandoned, the curvature is positive.
The escape-velocity zero-curvature universe has an interesting property -- it has zero net energy, i.e. gravitational potential energy is exactly balanced by kinetic energy. This means the universe can appear spontaneously, like quantum virtual particle do, but on a larger scale.
"Because there is a law such as gravity, the universe can and will create itself from nothing ... Spontaneous creation is the reason there is something rather than nothing, why the universe exists, why we exist." — Stephen Hawking in "The Grand Design".
I'm not qualified to say what a negative curvature might do to that pretty spontaneous-creation picture. It's a nice model, and it offers an answer to the question "where did all this come from?"
- pdonis 13y agoAs I understand it, for a universe that's being uniformly accelerated, by for example dark energy, its overall curvature should be negative. By "overall curvature", do you mean spacetime curvature, or the curvature of a spatial slice? As I said in my previous post, the de Sitter spacetime, which is the model for a universe that is being uniformly accelerated, has uniform positive spacetime curvature. These Wikipedia links give a good overview (of course Wikipedia is not always reliable, but these pages appear to be consistent with what I read in other more knowledgeable sources such as GR textbooks): http://en.wikipedia.org/wiki/De_Sitter_universe http://en.wikipedia.org/wiki/De_Sitter_universe http://en.wikipedia.org/wiki/De_Sitter_space http://en.wikipedia.org/wiki/De_Sitter_space The spacetime curvature scalar R is 4 Lambda, where Lambda is the (positive) cosmological constant. The second Wikipedia link also describes the different possible spatial slicings of de Sitter spacetime; as I noted previously, slicings exist with all three types of spatial curvature (positive, zero, and negative). However, it is true that the slicing with negative curvature is the one that's used in the standard cosmological models of a universe that is dark energy dominated; that's the FLRW model with exponential expansion that's discussed in the first Wikipedia link. So if that specifically is what you were referring to by negative "overall curvature", then I agree; but I would specify that it's overall negative spatial curvature, and that that model assumes a particular spatial slicing which is not the only possible one.
- lutusp 13y ago> By "overall curvature", do you mean spacetime curvature, or the curvature of a spatial slice? I'm referring to the overall spacetime curvature shared by the universe as a whole. > ... and that that model assumes a particular spatial slicing which is not the only possible one. Sorry, out of my depth.
- pdonis 13y agoI'm referring to the overall spacetime curvature shared by the universe as a whole. Then that's positive, not negative, for a spacetime dominated by dark energy. The curvature that is negative is the curvature of the spatial slices in the model used in cosmology for a dark energy dominated universe--more precisely, in the model referred to in the article as being suggested by the new data.