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Cosmology

A circumscribed Universe

Nature volume 392, pages 24–25 (1998)Cite this article

Our Universe occupies space. But what sort of space? Mathematicians call different types of space ‘manifolds’, and characterize them by two properties: by the local curvature — geometry; and the overall shape — topology. Most cosmologists are concerned only with the curvature, as it is directly related to the mass in the Universe (and therefore it is observable), and because it determines the past and future evolution of the Universe with time. The global shape is not, in general, prescribed by geometry, but it also is observable: topological information is imprinted on the fluctuations of the cosmic microwave background. This has already provided some evidence that the Universe is infinite or, at least, not small compared with the distance we can see. But now Cornish, Spergel and Starkman1,2 have realized that the Universe can still be finite, and relatively small, if its curvature is negative. Moreover, we may soon be able to measure its size and shape. This question of whether the Universe is finite has profound implications for its birth.

Cosmologists classify the curvature of the Universe as positive, zero or negative. Flat, euclidean space, called ℝ3, has zero curvature — the sum of internal angles of a triangle drawn on it is 180°. With positive curvature, as on a sphere, the sum of the angles is more than 180°, and with negative it is less. Einstein's equation relates the curvature to the amount of mass present in the Universe (assuming that the energy density of empty space — the cosmological constant — is zero). The sign of the curvature depends on whether the average mass density at present is more than about 2×10−29 g cm−3, the critical density.

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Figure 1: A sphere intersects cubic domains.

GLENN STARKMAN

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Authors and Affiliations

  1. Institute for Cosmic Ray Research, University of Tokyo, Tanashi, 188, Tokyo, Japan

    Masataka Fukugita

  2. Institute for Advanced Study, Princeton, New Jersey, 08540, USA

    Masataka Fukugita

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  1. Masataka Fukugita
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Fukugita, M. A circumscribed Universe. Nature 392, 24–25 (1998). https://doi.org/10.1038/32053

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