Green Functions for Topology Change

Details Green Functions for Topology Change Green Functions for Topology Change

2000-06-28

arxiv.org/abs/gr-qc/0006096v2

JHEP 0503:060,2005

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

11 pages, 2 figures, reshaped version

Scientific paper

10.1088/1126-6708/2005/03/060

We explicitly calculate the Green functions describing quantum changes of topology in Friedman-Lemaitre-Robertson-Walker Universes whose spacelike sections are compact but endowed with distinct topologies. The calculations are performed using the long wavelength approximation at second order in the gradient expansion. We argue that complex metrics are necessary in order to obtain a non-vanishing Green functions and interpret this fact as demonstrating that a quantum topology change can be viewed as a quantum tunneling effect. We demonstrate that quantum topological transitions between curved hypersurfaces are allowed whereas no transition to or from a flat section is possible, establishing thus a selection rule. We also show that the quantum topology changes in the direction of negatively curved hypersurfaces are strongly enhanced as time goes on, while transitions in the opposite direction are suppressed.

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