4D QUANTUM DILATON GRAVITY DURING INFLATION AND RENORMALIZATION AT ONE-LOOP

We consider 4D quantum dilaton gravity with the most general coupling in a homogeneous and isotropic universe, in particular an inflationary one, which is essentially characterized by an exponentially expanding scale factor with time. We show that on the inflationary background t his theory can be miraculously renormalized, at least at the one-loop level This theory must be an effective theory during the inflation of the un-constructed complete quantum theory of gravity.