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东方天遥至尊木虫 (著名写手)
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【交流】The cosmic topology V.S. inflation
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The comic topology is the global property of the universe, so it cannot be derived from general relativity. The reason for that is general relativity is a kind of theory which describes the local properties of spacetime. The topology of the universe can only be imposed by hand. There is so-called "small universe", which refers to a kind of spacetime that is obtained by identification. Via identification, the universe gains the non-trivial topology. In this case, even though the spatial curvature of the universe is zero or -1---for the usual Friedmann universe, which correspond to flat or hyperbolic universe, whose volumes are infinite---the volume of the universe is finite! Let me just explain what Friedmann universe is. In some sense, it is just our universe. We believe that at any time, and at any point, the universe looks the same in any direction. That is to say, the universe is homogeneous and isotropic spatially. But from the observation, we know that the universe is expanding. So temporally, it isn't homogeneous. There are three different kinds of homogeneous, isotropic spaces: closed, flat and open, with spatial curvatures equal to +1, 0, and -1, respectively. In the case of de Sitter spacetime, one solution of Einstein's equation, the situation is much different. De Sitter spacetime is sort of manifold with a positive 4-curvature constant, that is to say, it is homogeneous and isotropic spatially and temporally. In the old inflationary cosmology, Alen Guth assumed that the expansion of the universe is driven by the false vacuum energy which acts like the cosmological constant. Therefore, the universe undergoes exponential expansion, and the metric of the universe is that of de Sitter spacetime. So the universe is homogeneous and isotropic spatially and temporally. Then we have the right to choose special coordinate to express the its metric in the form of closed, flat or open universe! So, inflation in a de Sitter universe makes no sense. |
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