Flow equation of quantum Einstein gravity in a higher-derivative truncation

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 properties of the 3-dimensional flow are investigated, and they are confronted with those of the 2-dimensional Einstein-Hilbert flow. The non-Gaussian fixed point predicted by the latter is found to generalize to a fixed point on the enlarged theory space. In order to test the reliability of the R 2 -truncation near this fixed point 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 fixed point 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 fixed point is not afflicted with this problem. Also the Gaussian fixed point of the Einstein-Hilbert truncation is analyzed; it turns out that it does not generalize to a corresponding fixed point on the enlarged theory space.

Gauges and functional measures in quantum gravity II: higher-derivative gravity

“…These are all the divergences that arise at one loop in d = 4. The method we have used is a one-loop approximation of the single-field approximation of the exact RG equation for gravity, as first derived in [31] for the EH-case and then extended to HDG in [24,[34][35][36], to 3d topologically massive gravity in [40], and beyond the one-loop approximation in [41][42][43][44].…”

Asymptotic Safety, Fractals, and Cosmology

“…As a consequence of the NGFP controlling the UV behavior of the theory, the four-dimensional graviton propagator essentially behaves two-dimensional on microscopic scales. Subsequently, the finger prints of the NGFP on the fabric of the effective QEG space-times have been discussed in [12], where it was shown that Asymptotic Safety induces a characteristic self-similarity of space-time on length-scales below the Planck length ℓ PL . The graviton propagator becomes scale-invariant in this regime [10].…”

Astrophysical implications of the Asymptotic Safety Scenario in Quantum Gravity

“…This mechanism is at the very heart of the "asymptotic safety" underlying the non-perturbative renormalizability of QEG. A detailed discussion of this mechanism is beyond the scope of the present review; the reader it referred to [6,7,40,48]. Suffice it to say that the quantum mechanical generation of the primordial fluctuations happens on sub-Hubble distance scales.…”

“…The gravitational antiscreening behavior is very similar to the running of the non-Abelian gauge coupling in Yang-Mills Theory, but only after the introduction of the effective average action and its functional renormalization group equation for gravity [4] detailed investigations of the scaling behavior of the Newtons's constant have become possible [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. The non-perturbative renormalization group equation underlying this approach defines a Wilsonian RG flow on a theory space which consists of all diffeomorphism invariant functionals of the metric g µν .…”