Green Functions for Topology Change

TL;DR

This paper calculates Green functions for quantum topology changes in closed cosmological models, revealing that such transitions resemble quantum tunneling and are subject to specific geometric constraints.

Contribution

It provides explicit calculations of Green functions for quantum topology change in cosmology, highlighting the necessity of complex metrics and establishing a selection rule for transitions.

Findings

Quantum topology change can be viewed as quantum tunneling.

Transitions are allowed between curved hypersurfaces but not flat ones.

Negative curvature transitions are enhanced over time.

Abstract

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.