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

The authors calculate the one-loop approximation to the Euclidean quantum gravity coupled to a scalar field around the classical Carlini and Mijic (CM) wormhole solutions (1990). 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 inclusions of a bare cosmological constant to the case of a sphere S⁴ 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, the authors recover Coleman's exp(exp(1/ gamma _eff)) peak at the effective cosmological constant gamma _eff=0, with no phase ambiguities in Z_EQG.