One-loop Vilkovisky-DeWitt effective potential for scale-invariant gravity

Abstract

For a pure gravity theory without matter, the scale symmetric phase represents an equivalent class of gravity theories, to which the Einstein gravity plus a cosmological constant belongs under a special gauge choice. The one-loop quantum correction of this scale-invariant theory is calculated by using Vilkovisky-DeWitt's method. It is shown that the resulting effective potential is gauge-independent as expected. Some discussions of the Vilkovisky-DeWitt method through this calculation are given.