Why the Cosmological Constant Seems to Hardly Care About Quantum Vacuum Fluctuations: Surprises From Background Independent Coarse Graining

Background Independence is a sine qua non for every satisfactory theory of Quantum Gravity. In particular if one tries to establish a corresponding notion of Wilsonian renormalization, or coarse graining, it presents a major conceptual and technical difficulty usually. In this paper we adopt the approach of the gravitational Effective Average Action and demonstrate that generically coarse graining in Quantum Gravity and in standard field theories on a non-dynamical spacetime are profoundly different. By means of a concrete example, which in connection with the cosmological constant problem is also interesting in its own right, we show that the surprising and sometimes counterintuitive implications of Background Independent coarse graining are neither restricted to high energies, nor to strongly nonperturbative regimes. In fact, while our approach has been employed in most studies of Asymptotic Safety, this particular ultraviolet behaviour plays no essential role in the present context.