What shape is space? On page 593 of this issue, Luminet et al. suggest that the topology of the Universe may be a 'Poincare dodecahedral space' ― as illustrated on this week's cover. And this is no idle abstraction: Luminet et al. show that this topology, unlike many others, is supported by data from NASA's Wilkinson Microwave Anisotropy Probe (WMAP), published earlier this year. In thinking about the large-scale shape of the Universe, three interlinked questions must be confronted. First, what is its spatial curvature? There are three possible answers. Three-dimensional sections of space-time may be 'flat' ― in such space sections, parallel lines stay the same distance apart and never meet (as in Euclidean space). Or the space sections may be 'negatively curved', such that parallel lines diverge from one another and never meet (the three-dimensional analogue of a Lobachevsky space). Finally, they may be 'positively curved', such that parallel lines converge and eventually intersect (the three-dimensional analogue of the surface of a sphere). The particular case that exists depends on how well the amount of matter in the Universe, coupled with the driving force of dark energy, balances the Universe's kinetic energy of expansion. This is usually expressed in terms of the normalized density parameter Ω_0, which is unity for flat space sections; for positive spatial curvature, Ω_0 is greater than one.
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