The phase of scalar field wormholes at one loop in the path integral formulation for Euclidean quantum gravity

TL;DR

This paper computes the one-loop Euclidean quantum gravity partition function around scalar field wormholes, showing it remains real in the little wormhole limit and discussing stability and cosmological implications.

Contribution

It provides the first one-loop calculation of the Euclidean quantum gravity partition function around scalar wormholes, demonstrating its reality and stability properties.

Findings

Partition functional is real in the little wormhole limit.

Inclusion of a cosmological constant can stabilize scalar modes.

Recovers Coleman's peak at zero effective cosmological constant.

Abstract

We here calculate the one-loop approximation to the Euclidean Quantum Gravity coupled to a scalar field around the classical Carlini and Miji\'c wormhole solutions. The main result is that the Euclidean partition functional $Z_{EQG}$ in the ``little wormhole'' limit is real. Extension of the CM solutions with the inclusion of a bare cosmological constant to the case of a sphere $S^4$ can lead to the elimination of the destabilizing effects of the scalar modes of gravity against those of the matter. In particular, in the asymptotic region of a large 4-sphere, we recover the Coleman's $\exp \left (\exp \left ({1\over \lambda_{eff}}\right )\right )$ peak at the effective cosmological constant $\lambda_{eff}=0$, with no phase ambiguities in $Z_{EQG}$.