Bimetric truncations for quantum Einstein gravity and asymptotic safety

In the average action approach to the quantization of gravity the fundamental requirement of “background independence” is met by actually introducing a background metric but leaving it completely arbitrary. The associated Wilsonian renormalization group defines a coarse graining flow on a theory space of functionals which, besides the dynamical metric, depend explicitly on the background metric. All solutions to the truncated flow equations known to date have a trivial background field dependence only, namely via the classical gauge fixing term. In this paper, we analyze a number of conceptual issues related to the bimetric character of the gravitational average action and explore a first nontrivial bimetric truncation in the simplified setting of conformally reduced gravity. Possible implications for the Asymptotic Safety program and the cosmological constant problem are discussed in detail.