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Hey all - I'm trying to get a better qualitative understanding of de Sitter space, and I'm a bit confused about the de Sitter universe. I've always seen it mathematically as a hyperboloid embedded in a higher-dimensional Minkowski space (with some annoying metric I've forgotten) but I've read (alright, fine, on Wikipedia :P) that a patch of de Sitter universe can be expressed as an FRW cosmology with a(t) = exp(Ht) - So... under that description, why is the de Sitter metric not just an FRW metric with that scale factor?