Abstract. 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.

Key words: Models of Quantum Gravity; Cosmology of Theories beyond the SM

E-print number: gr-qc/0006096
Cited: by
Refers: to

Received 6 August 2004, accepted for publication 22 March 2005
Published 26 April 2005