Background Independence and Asymptotic Safety in Conformally Reduced Gravity

Understand

We analyze the conceptual role of background independence in the application of the effective average action to quantum gravity.

• Insisting on a background independent renormalization group (RG) flow the coarse graining operation must be defined in terms of an unspecified variable metric since no rigid metric of a fixed background spacetime is available.
• This leads to an extra field dependence in the functional RG equation and a significantly different RG flow in comparison to the standard flow equation with a rigid metric in the mode cutoff.
• The background independent RG flow can possess a non-Gaussian fixed point, for instance, even though the corresponding standard one does not.