Is Quantum Einstein Gravity Nonperturbatively Renormalizable?

We find considerable evidence supporting the conjecture that four-dimensional Quantum Einstein Gravity is ``asymptotically safe'' in Weinberg's sense. This would mean that the theory is likely to be nonperturbatively renormalizable and thus could be considered a fundamental (rather than merely effective) theory which is mathematically consistent and predictive down to arbitrarily small length scales. For a truncated version of the exact flow equation of the effective average action we establish the existence of a non-Gaussian renormalization group fixed point which is suitable for the construction of a nonperturbative infinite cutoff-limit. The truncation ansatz includes the Einstein-Hilbert action and a higher derivative term.Comment: 18 pages, latex, 3 figure

Improved Action Functionals in Non-Perturbative Quantum Gravity

Models of gravity with variable G and Lambda have acquired greater relevance after the recent evidence in favour of the Einstein theory being non-perturbatively renormalizable in the Weinberg sense. The present paper builds a modified Arnowitt-Deser-Misner (ADM) action functional for such models which leads to a power-law growth of the scale factor for pure gravity and for a massless phi**4 theory in a Universe with Robertson-Walker symmetry, in agreement with the recently developed fixed-point cosmology. Interestingly, the renormalization-group flow at the fixed point is found to be compatible with a Lagrangian description of the running quantities G and Lambda.Comment: Latex file. Record without file already exists on SLAC-SPIRES, and hence that record and the one for the present arxiv submission should become one record onl

Ghost wave-function renormalization in Asymptotically Safe Quantum Gravity

Motivated by Weinberg's asymptotic safety scenario, we investigate the gravitational renormalization group flow in the Einstein-Hilbert truncation supplemented by the wave-function renormalization of the ghost fields. The latter induces non-trivial corrections to the beta-functions for Newton's constant and the cosmological constant. The resulting ghost-improved phase diagram is investigated in detail. In particular, we find a non-trivial ultraviolet fixed point in agreement with the asymptotic safety conjecture, which also survives in the presence of extra dimensions. In four dimensions the ghost anomalous dimension at the fixed point is $\eta_c^* = -1.8$, supporting space-time being effectively two-dimensional at short distances.Comment: 23 pages, 4 figure

A Class of Renormalization Group Invariant Scalar Field Cosmologies

We present a class of scalar field cosmologies with a dynamically evolving Newton parameter $G$ and cosmological term $\Lambda$. In particular, we discuss a class of solutions which are consistent with a renormalization group scaling for $G$ and $\Lambda$ near a fixed point. Moreover, we propose a modified action for gravity which includes the effective running of $G$ and $\Lambda$ near the fixed point. A proper understanding of the associated variational problem is obtained upon considering the four-dimensional gradient of the Newton parameter.Comment: 10 pages, RevTex4, no figures, to appear on GR

Background Independence and Asymptotic Safety in Conformally Reduced Gravity

We analyze the conceptual role of background independence in the application of the effective average action to quantum gravity. Insisting on a background independent renormalization group (RG) flow the coarse graining operation must be defined in terms of an unspecified variable metric since no rigid metric of a fixed background spacetime is available. This leads to an extra field dependence in the functional RG equation and a significantly different RG flow in comparison to the standard flow equation with a rigid metric in the mode cutoff. The background independent RG flow can possess a non-Gaussian fixed point, for instance, even though the corresponding standard one does not. We demonstrate the importance of this universal, essentially kinematical effect by computing the RG flow of Quantum Einstein Gravity in the ``conformally reduced'' Einstein--Hilbert approximation which discards all degrees of freedom contained in the metric except the conformal one. Without the extra field dependence the resulting RG flow is that of a simple $\phi^4$-theory. Including it one obtains a flow with exactly the same qualitative properties as in the full Einstein--Hilbert truncation. In particular it possesses the non-Gaussian fixed point which is necessary for asymptotic safety.Comment: 4 figures

The Renormalization Group, Systems of Units and the Hierarchy Problem

In the context of the Renormalization Group (RG) for gravity I discuss the role of field rescalings and their relation to choices of units. I concentrate on a simple Higgs model coupled to gravity, where natural choices of units can be based on Newton's constant or on the Higgs mass. These quantities are not invariant under the RG, and the ratio between the units is scale-dependent. In the toy model, strong RG running occurs in the intermediate regime between the Higgs and the Planck scale, reproducing the results of the Randall-Sundrum I model. Possible connections with the problem of the mass hierarchy are pointed out.Comment: Plain TEX, 16 pages. Some revisions, some references adde

Scale-dependent metric and causal structures in Quantum Einstein Gravity

Within the asymptotic safety scenario for gravity various conceptual issues related to the scale dependence of the metric are analyzed. The running effective field equations implied by the effective average action of Quantum Einstein Gravity (QEG) and the resulting families of resolution dependent metrics are discussed. The status of scale dependent vs. scale independent diffeomorphisms is clarified, and the difference between isometries implemented by scale dependent and independent Killing vectors is explained. A concept of scale dependent causality is proposed and illustrated by various simple examples. The possibility of assigning an "intrinsic length" to objects in a QEG spacetime is also discussed.Comment: 52 page

Noncommutative Geometry and the standard model with neutrino mixing

We show that allowing the metric dimension of a space to be independent of its KO-dimension and turning the finite noncommutative geometry F-- whose product with classical 4-dimensional space-time gives the standard model coupled with gravity--into a space of KO-dimension 6 by changing the grading on the antiparticle sector into its opposite, allows to solve three problems of the previous noncommutative geometry interpretation of the standard model of particle physics: The finite geometry F is no longer put in "by hand" but a conceptual understanding of its structure and a classification of its metrics is given. The fermion doubling problem in the fermionic part of the action is resolved. The spectral action of our joint work with Chamseddine now automatically generates the full standard model coupled with gravity with neutrino mixing and see-saw mechanism for neutrino masses. The predictions of the Weinberg angle and the Higgs scattering parameter at unification scale are the same as in our joint work but we also find a mass relation (to be imposed at unification scale).Comment: Typos removed, to appear in JHE

The Accelerated expansion of the Universe as a crossover phenomenon

We show that the accelerated expansion of the Universe can be viewed as a crossover phenomenon where the Newton constant and the Cosmological constant are actually scaling operators, dynamically evolving in the attraction basin of a non-Gaussian infrared fixed point, whose existence has been recently discussed. By linearization of the renormalized flow it is possible to evaluate the critical exponents, and it turns out that the approach to the fixed point is ruled by a marginal and a relevant direction. A smooth transition between the standard Friedmann--Lemaitre--Robertson--Walker (FLRW) cosmology and the observed accelerated expansion is then obtained, so that $\Omega_M \approx \Omega_\Lambda$ at late times.Comment: 12 pages, latex, use bibtex. In the final version, the presentation has been improved, and new references have been adde

Infrared fixed point in quantum Einstein gravity

We performed the renormalization group analysis of the quantum Einstein gravity in the deep infrared regime for different types of extensions of the model. It is shown that an attractive infrared point exists in the broken symmetric phase of the model. It is also shown that due to the Gaussian fixed point the IR critical exponent $\nu$ of the correlation length is 1/2. However, there exists a certain extension of the model which gives finite correlation length in the broken symmetric phase. It typically appears in case of models possessing a first order phase transitions as is demonstrated on the example of the scalar field theory with a Coleman-Weinberg potential.Comment: 9 pages, 7 figures, final version, to appear in JHE