The role of background independence for asymptotic safety in Quantum Einstein Gravity

We discuss various basic conceptual issues related to coarse graining flows in quantum gravity. In particular, the requirement of background independence is shown to lead to renormalization group (RG) flows which are significantly different from their analogs on a rigid background spacetime. The importance of these findings for the asymptotic safety approach to Quantum Einstein Gravity (QEG) is demonstrated in a simplified setting where only the conformal factor is quantized. We identify background independence as a (the?) key prerequisite for the existence of a non-Gaussian RG fixed point and the renormalizability of QEG.