Asymptotic safety of quantum gravity beyond Ricci scalars

Abstract

We investigate the asymptotic safety conjecture for quantum gravity including curvature invariants beyond Ricci scalars. Our strategy is put to work for families of gravitational actions which depend on functions of the Ricci scalar, the Ricci tensor, and products thereof. Combining functional renormalization with high order polynomial approximations and full numerical integration we derive the renormalization group flow for all couplings and analyse their fixed points, scaling exponents, and the fixed point effective action as a function of the background Ricci curvature. The theory is characterized by three relevant couplings. Higher-dimensional couplings show near-Gaussian scaling with increasing canonical mass dimension. We find that Ricci tensor invariants stabilize the UV fixed point and lead to a rapid convergence of polynomial approximations. We apply our results to models for cosmology and establish that the gravitational fixed point admits inflationary solutions. We also compare findings with those from fðRÞ-type theories in the same approximation and pin-point the key new effects due to Ricci tensor interactions. Implications for the asymptotic safety conjecture of gravity are indicated.

Aspects of asymptotic safety for quantum gravity

“…This covers Einstein Hilbert approximations and variants thereof , numerous higher curvature extensions [13,, and the inclusion of matter (see [101] for a recent review). High-order studies have also revealed that quantum gravity becomes "as Gaussian as it gets", meaning mostly weakly coupled except for a few dominant interactions [13,59,71]. In a similar vein, for general 4d quantum field theories without gravity, strict conditions and no-go theorems for asymptotic safety at weak coupling have also been found [102,103].…”

Zooming in on fermions and quantum gravity

“…Instead, it can be viewed as a criterion that distinguishes nonperturbative from near-perturbative fixed points. Other hints at a near-perturbative nature of the Reuter fixed point consist in the near-canonical scaling spectrum of higher-order curvature operators [14,[22][23][24] which is also exhibited by σ in our system, and the possibility to uncover the fixed point within one-loop perturbation theory [76,77]. Further, the Reuter fixed point might be connected continuously to the perturbative asymptotically safe fixed point seen within the epsilon expansion around d = 2 dimensions [1,78].…”

f(R,Rμν2) at one loop

“…The classically equivalent scalar-tensor theories have been studied for example in [45]. Recently there has also been work on Lagrangians of the form fðR μν R μν Þ þ RZðR μν R μν Þ [46]. In this paper we will consider more general theories depending on the Ricci scalar and the square of the Ricci tensor…”