Cotsakis et al. [Phys. Rev. D 49, 6489 (1994)] claimed that wormhole solutions can be obtained with real scalar fields which could in turn be simulated with higher order gravity theories. Because of various sign errors this conclusion is not justified, and instead a complex scalar field is necessary. Higher derivative theories can have wormholes by choosing the “wrong signs” for the coefficients in front of the functions of scalar curvature. This ensures that there is a minus sign in front of the kinetic term in the conformally related scalar field theory, thus ensuring that the Ricci tensor has negative eigenvalues. A real scalar field with a negative definite potential $V\left(\phi \right)<\mathrm{}0\mathrm{}$, although satisfying the Ricci tensor condition, does not support a wormhole, at least when using a FRW metric.

• Received 7 August 1995

DOI:https://doi.org/10.1103/PhysRevD.55.6606