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Wikipedia says that inflation is the exponential expansion of space in the early universe.I'm trying to have a physical picture of this.Given that I can't visualize 3+1 pseudoriemannian manifolds,I'm trying to understand the situation for 2+1 pseudoriemannian manifolds. Can we embed 2+1 space-time of GR in a 4 Dimensional flat Euclidean space ?

unruh
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Quark
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I don't see why not. In fact one nice way to generate certain symmetric spacetimes is to embed them in higher dimensional space then constrain your variables to the manifold and massage the induced metric into something palatable. So I'm going to do you one better: I'm going to embed a 1+1 GR spacetime in 3D Euclidean space. The best example I can come up with off the top of my head is de Sitter space, which actually works as a good expanding universe model (which I will hedge by pointing out that this only matches the FRW metric in certain limits). de Sitter space is basically the Minkowski version of a sphere, where we fix the Minkowski distance squared of any point in $dS^N$ from the origin of $\mathbb{R}^{N,1}$ to be a constant, then massage the induced metric. $dS^2$ is then a hyperboloid of one sheet.

Jordan
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