Vilkovisky-DeWitt effective potential for Einstein gravity coupled to scalars

The Vilkovisky-DeWitt one-loop effective potential is constructed for Einstein gravity coupled nonminimally to scalars, and is proved explicitly to be independent of gauge choice, for a class of covariant gauges. Explicit forms of the effective potential in three cases are given. The first two cases are used to show that the Vilkovisky-DeWitt formalism is not just a gauge-fixed version of the conventional one in general. The last case concerns the possibility of inducing Einstein gravity dynamically in a Brans-Dicke-type model