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

For a pure gravity theory without matter, the scale symmetric phase represe nts 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 usi ng Vilkovisky-DeWitt's method. It is shown that the resulting effective pot ential is gauge-independent as expected. Some discussions of the Vilkovisky -DeWitt method through this calculation are given.