MINIMALLY COUPLED SCALAR FIELD WORMHOLES

We examine conditions for the existence of wormhole solutions in the E instein equations with a dynamical minimally coupled scalar field matt er source with an arbitrary effective potential. We find three wormhol e solutions which connect a baby universe with two asymptotically flat spaces through a narrow tube in a constant, cosinelike, and SIGMA(i=0 )c(i)a(-i) potential, respectively (a being the scale factor). Because of the fact that the scalar field is not constant inside these wormho les, the gravitational constant takes different values in the two asym ptotically flat spaces. These wormholes, under a conformal transformat ion, may be regarded as instanton-type solutions in higher order gravi ty with a Lagrangian that is an arbitrary analytic function of the sca lar curvature.