Abstract
We examine conditions for the existence of wormhole solutions in the Einstein equations with a dynamical minimally coupled scalar field matter source with an arbitrary effective potential. We find three wormhole solutions which connect a baby universe with two asymptotically flat spaces through a narrow tube in a constant, cosinelike, and $\ensuremath{\Sigma}{i=0}^{3}{c}_{i}{a}^{\ensuremath{-}i}$ potential, respectively ($a$ being the scale factor). Because of the fact that the scalar field is not constant inside these wormholes, the gravitational constant takes different values in the two asymptotically flat spaces. These wormholes, under a conformal transformation, may be regarded as instanton-type solutions in higher order gravity with a Lagrangian that is an arbitrary analytic function of the scalar curvature.
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