RG flows of Quantum Einstein Gravity on maximally symmetric spaces

Understand

We use the Wetterich-equation to study the renormalization group flow of $f(R)$-gravity in a three-dimensional, conformally reduced setting.

• Building on the exact heat kernel for maximally symmetric spaces, we obtain a partial differential equation which captures the scale-dependence of $f(R)$ for positive and, for the first time, negative scalar curvature.
• The effects of different background topologies are studied in detail and it is shown that they affect the gravitational RG flow in a way that is not visible in finite-dimensional truncations.
• Thus, while featuring local background independence, the functional renormalization group equation is sensitive to the topological properties of the background.