Real tunneling geometries and the large-scale topology of the universe

Journal Article · Mon Oct 15 00:00:00 EDT 1990 · Physical Review, D (Particles Fields); (USA)

DOI:https://doi.org/10.1103/PhysRevD.42.2458· OSTI ID:6223184

Gibbons, G W ^[1]; Hartle, J B ^[2]

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1. Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge (United Kingdom)
2. Department of Physics, University of California, Santa Barbara, CA (USA)

If the topology and geometry of spacetime are quantum-mechanically variable, then the particular classical large-scale topology and geometry observed in our universe must be statistical predictions of its initial condition. This paper examines the predictions of the no boundary'' initial condition for the present large-scale topology and geometry. Finite-action real tunneling solutions of Einstein's equation are important for such predictions. These consist of compact Riemannian (Euclidean) geometries joined to a Lorentzian cosmological geometry across a spacelike surface of vanishing extrinsic curvature. The classification of such solutions is discussed and general constraints on their topology derived. For example, it is shown that, if the Euclidean Ricci tensor is positive, then a real tunneling solution can nucleate only a single connected Lorentzian spacetime (the unique conception theorem). Explicit examples of real tunneling solutions driven by a cosmological constant are exhibited and their implications for cosmic baldness described. It is argued that the most probable large-scale spacetime predicted by the real tunneling solutions of the no-boundary'' initial condition has the topology {bold R}{times}{ital S}{sup 3} with the de Sitter metric.

• OSTI ID: 6223184
• Journal Information: Physical Review, D (Particles Fields); (USA), Vol. 42:8; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
UNIVERSE
QUANTUM MECHANICS
TOPOLOGY
BOUNDARY CONDITIONS
COSMOLOGICAL MODELS
EINSTEIN FIELD EQUATIONS
EUCLIDEAN SPACE
RICCI TENSOR
RIEMANN SPACE
SPACE-TIME
TUNNEL EFFECT
WAVE FUNCTIONS
EQUATIONS
FIELD EQUATIONS
FUNCTIONS
MATHEMATICAL MODELS
MATHEMATICAL SPACE
MATHEMATICS
MECHANICS
SPACE
TENSORS
640106* - Astrophysics & Cosmology- Cosmology
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