Flow Equation of Quantum Einstein Gravity in a Higher-Derivative Truncation

TL;DR

This paper investigates the renormalization group flow of Quantum Einstein Gravity with an added $R^2$ term, finding evidence for a non-Gaussian fixed point that suggests the theory may be nonperturbatively renormalizable and asymptotically safe.

Contribution

It extends the Einstein-Hilbert truncation by including a higher-derivative $R^2$ term and analyzes the fixed point structure, scheme dependence, and consistency of the results.

Findings

Identification of a non-Gaussian fixed point in the extended theory space.

Weak scheme dependence of universal quantities near the fixed point.

High numerical agreement between different truncations, supporting the fixed point's physical relevance.

Abstract

Motivated by recent evidence indicating that Quantum Einstein Gravity (QEG) might be nonperturbatively renormalizable, the exact renormalization group equation of QEG is evaluated in a truncation of theory space which generalizes the Einstein-Hilbert truncation by the inclusion of a higher-derivative term $(R^2)$. The beta-functions describing the renormalization group flow of the cosmological constant, Newton's constant, and the $R^2$-coupling are computed explicitly. The fixed point (FP) properties of the 3-dimensional flow are investigated, and they are confronted with those of the 2-dimensional Einstein-Hilbert flow. The non-Gaussian FP predicted by the latter is found to generalize to a FP on the enlarged theory space. In order to test the reliability of the $R^2$-truncation near this FP we analyze the residual scheme dependence of various universal quantities; it turns out to be very weak. The two truncations are compared in detail, and their numerical predictions are found to agree with a suprisingly high precision. Due to the consistency of the results it appears increasingly unlikely that the non-Gaussian FP is an artifact of the truncation. If it is present in the exact theory QEG is probably nonperturbatively renormalizable and ``asymptotically safe''. We discuss how the conformal factor problem of Euclidean gravity manifests itself in the exact renormalization group approach and show that, in the $R^2$-truncation, the investigation of the FP is not afflicted with this problem. Also the Gaussian FP of the Einstein-Hilbert truncation is analyzed; it turns out that it does not generalize to a corresponding FP on the enlarged theory space.