Vilkovisky-DeWitt effective potential for higher-derivative gravity coupled to scalars

Using a four-parameter family of gauges, the one-loop Vilkovisky-DeWitt effective potential for higher-derivative gravity coupled to scalars about a flat background spacetime is constructed. It is shown explicitly to be independent of the gauge parameters. The effective potential is then evaluated at finite temperature which is used to investigate the possibility of inducing Einstein gravity spontaneously. The critical temperature for this phase transition is also estimated. This phase transition, if it exists, will occur in the early Universe between the grand-unified-theory and the Planck scales, and may be a candidate for the primordial inflationary universe scenario.