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

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

Oct 1990

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1990phrvd..42.2458g&link_type=abstract

Physical Review D (Particles and Fields), Volume 42, Issue 8, 15 October 1990, pp.2458-2468

Mathematics

Logic

115

Origin And Formation Of The Universe, Fundamental Problems And General Formalism

Scientific paper

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 R×S3 with the de Sitter metric.

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