Euclidean Quantum Wormholes with Scalar Fields

Abstract

We consider the quantum analogs of Euclidean wormholes obtained by Carlini and Mijić (CM), who analytically continued recollapsing closed universe models. Using a perfect fluid matter source, we obtain asymptotically Euclidean (AE) wormholes when the strong energy condition is satisfied. Such wormholes are found to be consistent with the Hawking–Page (HP) conjecture for quantum wormholes as solutions of the Wheeler–DeWitt (WDW) equation. By simulating the equation of state of a perfect fluid with a real scalar field, quantum wormholes are also found when the strong energy condition is violated, although generally not AE. The non-AE solutions are interpreted as excited states of the quantum wormhole spectrum. Our results give support to the claim of HP that quantum wormhole solutions are a fairly general property of the WDW equation for various matter sources. Matter sources giving quantum wormholes could now include those expected in low energy effective string theory: a dilaton scalar field with exponential potential. This is unlike the classical case where such matter sources do not allow wormhole solutions. We finally contrast quantum wormhole solutions with other boundary conditions of quantum cosmology describing an inflationary earlier behavior and a resulting large Lorentzian universe phase.