As surveyed in the introduction, important evidence for the asymptotic safety scenario comes from the truncated flow of the effective average action, as computed from its functional renormalization flow equation (FRGE). In this section we use the term Quantum Einstein Gravity to refer to a version of Quantum Gravidynamics where the metric is used as the dynamical variable. The key results have been outlined in the introduction. Here we present in more detail the effective average action for gravity, its flow equation, and the results obtained from its truncations.

4.1 The effective average action for gravity and its FRGE

4.1.1 Properties of the effective average action

4.2 Geometries at different resolution scales

4.3 Truncated flow equations

4.4 Einstein–Hilbert and truncations

4.4.1 Phase portrait of the Einstein–Hilbert truncation

4.4.2 Evidence for asymptotic safety – Survey

4.4.3 Structure of the unstable manifold

4.4.4 Robustness of qualitative features

4.4.5 Comments on the full FRGE dynamics

4.1.1 Properties of the effective average action

4.2 Geometries at different resolution scales

4.3 Truncated flow equations

4.4 Einstein–Hilbert and truncations

4.4.1 Phase portrait of the Einstein–Hilbert truncation

4.4.2 Evidence for asymptotic safety – Survey

4.4.3 Structure of the unstable manifold

4.4.4 Robustness of qualitative features

4.4.5 Comments on the full FRGE dynamics

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