Gauge-independent effective potential for minimally coupled quantum fields in curved space

We calculate the effective potential to one-loop order for scalar and spinor fields minimally coupled to gravity by making a local expansion in powers of the curvature. Our calculations are done in the unitary gauge to third order in the Riemann tensor, using the geometrical background field method of Vilkovisky and DeWitt. The final result is gauge invariant as well as gauge condition independent