Contraints on Matter from Asymptotic Safety

Recent studies of the ultraviolet behaviour of pure gravity suggest that it admits a non-Gaussian attractive fixed point, and therefore that the theory is asymptotically safe. We consider the effect on this fixed point of massless minimally coupled matter fields. The existence of a UV attractive fixed point puts bounds on the type and number of such fields.Comment: 5 pages, 2 figures, revtex4; introduction expande

Asymptotic Safety of Gravity Coupled to Matter

Nonperturbative treatments of the UV limit of pure gravity suggest that it admits a stable fixed point with positive Newton's constant and cosmological constant. We prove that this result is stable under the addition of a scalar field with a generic potential and nonminimal couplings to the scalar curvature. There is a fixed point where the mass and all nonminimal scalar interactions vanish while the gravitational couplings have values which are almost identical to the pure gravity case. We discuss the linearized flow around this fixed point and find that the critical surface is four-dimensional. In the presence of other, arbitrary, massless minimally coupled matter fields, the existence of the fixed point, the sign of the cosmological constant and the dimension of the critical surface depend on the type and number of fields. In particular, for some matter content, there exist polynomial asymptotically free scalar potentials, thus providing a solution to the well-known problem of triviality.Comment: 18 pages,typeset with revtex

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

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

Renormalization group improved gravitational actions: a Brans-Dicke approach

A new framework for exploiting information about the renormalization group (RG) behavior of gravity in a dynamical context is discussed. The Einstein-Hilbert action is RG-improved by replacing Newton's constant and the cosmological constant by scalar functions in the corresponding Lagrangian density. The position dependence of $G$ and $\Lambda$ is governed by a RG equation together with an appropriate identification of RG scales with points in spacetime. The dynamics of the fields $G$ and $\Lambda$ does not admit a Lagrangian description in general. Within the Lagrangian formalism for the gravitational field they have the status of externally prescribed ``background'' fields. The metric satisfies an effective Einstein equation similar to that of Brans-Dicke theory. Its consistency imposes severe constraints on allowed backgrounds. In the new RG-framework, $G$ and $\Lambda$ carry energy and momentum. It is tested in the setting of homogeneous-isotropic cosmology and is compared to alternative approaches where the fields $G$ and $\Lambda$ do not carry gravitating 4-momentum. The fixed point regime of the underlying RG flow is studied in detail.Comment: LaTeX, 72 pages, no figure

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

Quantum cosmology with big-brake singularity

We investigate a cosmological model with a big-brake singularity in the future: while the first time derivative of the scale factor goes to zero, its second time derivative tends to minus infinity. Although we also discuss the classical version of the model in some detail, our main interest lies in its quantization. We formulate the Wheeler-DeWitt equation and derive solutions describing wave packets. We show that all such solutions vanish in the region of the classical singularity, a behaviour which we interpret as singularity avoidance. We then discuss the same situation in loop quantum cosmology. While this leads to a different factor ordering, the singularity is there avoided, too.Comment: 24 pages, 7 figures, figures improved, references added, conceptual clarifications include

The role of Background Independence for Asymptotic Safety in Quantum Einstein Gravity

We discuss various basic conceptual issues related to coarse graining flows in quantum gravity. In particular the requirement of background independence is shown to lead to renormalization group (RG) flows which are significantly different from their analogs on a rigid background spacetime. The importance of these findings for the asymptotic safety approach to Quantum Einstein Gravity (QEG) is demonstrated in a simplified setting where only the conformal factor is quantized. We identify background independence as a (the ?) key prerequisite for the existence of a non-Gaussian RG fixed point and the renormalizability of QEG.Comment: 2 figures. Talk given by M.R. at the WE-Heraeus-Seminar "Quantum Gravity: Challenges and Perspectives", Bad Honnef, April 14-16, 2008; to appear in General Relativity and Gravitatio

Primordial Entropy Production and Lambda-driven Inflation from Quantum Einstein Gravity

We review recent work on renormalization group (RG) improved cosmologies based upon a RG trajectory of Quantum Einstein Gravity (QEG) with realistic parameter values. In particular we argue that QEG effects can account for the entire entropy of the present Universe in the massless sector and give rise to a phase of inflationary expansion. This phase is a pure quantum effect and requires no classical inflaton field.Comment: 12 pages, 4 figures, IGCG-07 Pun