Abstract
Starting from an ultraviolet fixed point, we study the infrared behavior of quantum Weyl gravity in terms of a functional renormalization group (RG) flow equation. To do so, we employ two classes of Bach-flat backgrounds, namely maximally symmetric spacetimes and Ricci-flat backgrounds in the improved one-loop scheme. We show that in the absence of matter fields and with a topological term included, the effective action exhibits dynamical breaking of scale symmetry. In particular, it is shown that apart from a genuine IR fixed point that is reached at a zero-value of the running scale, the RG flow also exhibits bouncing behavior in the IR regime. We demonstrate that both $\beta_C$ and $\beta_E$ reach the RG turning point (almost) simultaneously at the same finite energy scale, irrespectively of the chosen background. The IR fixed point itself is found to be IR-stable in the space of the considered couplings. Ensuing scaling dimensions of both operators are also computed. Salient issues, including the connection of the observed bouncing RG flow behavior with holography and prospective implications in early Universe cosmology, are also briefly discussed.
Highlights
The current constraints from Planck measurements of the CMB anisotropies indicate that the cosmological perturbations are scale invariant with the value of the scalar spectral index ns 1⁄4 0.965 Æ 0.004 [1]
Apart from the fact that they are instrumental in providing a dynamical origin of mass scales [2,3,4,5,6,7,8], they have a number of further desirable features; for instance, they provide an appealing framework for addressing the hierarchy problem [9], lead to naturally flat inflationary potentials [10], furnish dark matter candidates [11,12] or even provide a viable alternative for dark matter itself [13,14,15]
III, we show that when the proper change of the integration measure under the functional integral (9) is employed, the fixings of gauges for both the diffeomorphism and conformal symmetry are done and the ensuing Faddeev-Popov determinant is taken into account, one obtains precisely 6 propagating degrees of freedom—as expected in the quantum Weyl gravity (QWG)
Summary
The current constraints from Planck measurements of the CMB anisotropies indicate that the cosmological perturbations are (nearly) scale invariant with the value of the scalar spectral index ns 1⁄4 0.965 Æ 0.004 (with a 68% confidence level) [1]. There is a strong hope that when the nontrivial FP is found the corresponding gravity theory will behave in a controllable way, and the FP will determine fully the nonperturbative spectrum, solve the problem with unitarity, and tame the divergences since the RG flow stops at the FP [45,46] This type of scenario (reinforced by a condition of a finite dimensionality of the critical surface on which assumed FP lies) is well-known from the QFT description of critical phenomena in condensed matter, where the non-Gaussian FP provides a welldefined theory in the UV (or IR) regime [47]. For the reader’s convenience, the paper is accompanied with Supplemental Material (SM) [52] that clarifies some technical and conceptual details needed in the main text
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