Background-metric independent formulation of 4D quantum gravity

Using the background-metric independence for the traceless mode as well as the conformal mode, 4D quantum gravity is described as a quantum field theo ry defined on a non-dynamical background metric. The measure then induces a n action with four derivatives. So we think that fourth order gravity is es sential and the Einstein-Hilbert term should be treated like a mass term. W e introduce the dimensionless self-coupling constant t for the traceless mo de. In this paper we study a model where the measure can be evaluated in th e limit t --> 0 exactly, using the background-metric independence for the c onformal mode. The t-dependence of the measure is determined perturbatively using the background-metric independence for the traceless mode. (C) 1999 Elsevier Science B.V. All rights reserved.