Conformal scalar field wormholes

The authors solve the Euclidian Einstein equations with a cosmological constant and a conformally coupled scalar field, taking the metric to be of the Robertson-Walker type. In the case Lambda =0, they find solutions which represent a wormhole connecting two asymptotically flat Euclidian regions. In the case Lambda >0, they find solutions which represent tunnelling from a small Tolman-like universe to a large Robertson-Walker universe. These solutions are qualitatively similar to those found, respectively, by Giddings and Strominger (1988), and by Myers (1988), using a third-rank antisymmetric tensor field. They differ in that the effective gravitational constant can become negative.