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Green functions for topology change

Jérôme Martin1, Nelson Pinto-Neto2 and Ivano Damião Soares2

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We explicitly calculate the Green functions describing quantum changes of topology in Friedman-Lemaître-Robertson-Walker universes the spacelike sections of which 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.

Keywords

Models of Quantum Gravity

Cosmology of Theories beyond the SM

 

E-print Number: gr-qc/0006096

Cited: by |

Refers: to

PACS

04.60.-m Quantum gravity

02.40.-k Geometry, differential geometry, and topology

02.30.Hq Ordinary differential equations

98.80.Cq Particle-theory and field-theory models of the early Universe (including cosmic pancakes, cosmic strings, chaotic phenomena, inflationary universe, etc.)

MSC

83Cxx General relativity

83F05 Cosmology

34B27 Green functions

Subjects

Mathematical physics

Gravitation and cosmology

Astrophysics and astroparticles

Dates

Issue 03 (March 2005)

Received 6 August 2004, accepted for publication 22 March 2005

Published 26 April 2005



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