G. Cognola, RENORMALIZATION OF THE ONE-LOOP EFFECTIVE ACTION ON AN ARBITRARY CURVED SPACE-TIME - A GENERAL-METHOD, Physical review. D. Particles and fields, 50(2), 1994, pp. 909-916
Using zeta-function regularization for the one-loop effective action,
we carry out the renormalization of the one-loop effective Lagrangian
for a self-interacting scalar field theory in an arbitrary gravitation
al background. We give very general expressions and recover known resu
lts as special cases.