## Big Sinhy Spheres in Space

OK, my title is really corny. Call it geek humour of the worst kind, if you want. But you’ll see where I’m coming from soon enough. In my last post, I was going over the three kinds of space that could be broadly consistent with a homogeneous distribution of matter; this leading to a criterion of uniform curvature. To review briefly, this yields either a universe of positive energy and negative curvature in the form of a 3-hyperbola or a universe of zero energy and zero curvature in the form of a Euclidean 3-space or a universe of negative total energy and positive curvature in...

Read More## Three kinds of space

Assume once more that space is homogeneous, at least at large scales; that is, for distances greater than (where , the Hubble distance is roughly 14 billion light-years). We know that below these scales, the distribution of ordinary matter appears to have a correlation dimension of around 1.77±0.04, implying a fractal structure similar to that of diffusion limited aggregation (DLA). But if the universe has a homogeneous distribution of matter at large scales, then we might think about it like, for example, the paved surface of a asphalt road. Stand back, and the surface is uniform; look...

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