Patching up the No-Boundary Proposal with virtual Euclidean wormholes

TL;DR

This paper addresses limitations of the No-Boundary Proposal in quantum cosmology by constructing continuous paths with virtual Euclidean wormholes, validating the approach and refining decay rate calculations.

Contribution

It introduces a method to connect disjoint instantons via virtual wormholes, improving the understanding of tunneling processes in quantum cosmology.

Findings

Constructed continuous paths connecting disjoint instantons.

Decay rates match in exponential factor with traditional methods.

Prefactors in decay rates are refined using the new approach.

Abstract

In quantum cosmology, one often considers tunneling phenomena which may have occurred in the early universe. Processes requiring quantum penetration of a potential barrier include black hole pair creation and the decay of vacuum domain walls. Ideally, one calculates the rates for such processes by finding an instanton, or Euclidean solution of the field equations, which interpolates between the initial and final states. In practice, however, it has become customary to calculate such amplitudes using the No-Boundary Proposal of Hartle and Hawking. A criticism of this method is that it does not use a single path which interpolates between the initial and final states, but two disjoint instantons: One divides the probability to create the final state from nothing by the probability to create the initial state from nothing and decrees the answer to be the rate of tunneling from the initial to the final state. Here, we demonstrate the validity of this approach by constructing continuous paths connecting the ingoing and outgoing data, which may be viewed as perturbations of the set of disconnected instantons. They are off-shell, but will still dominate the path integral as they have action arbitrarily close to the no-boundary action. In this picture, a virtual domain wall, or wormhole, is created and annihilated in such a way as to interface between the disjoint instantons. Decay rates calculated using our construction differ from decay rates calculated using the No-Boundary Proposal only in the prefactor; the exponent, which usually dominates the result, remains unchanged.