The Asymptotic Safety Scenario in Quantum Gravity -- An Introduction

The asymptotic safety program strives for a consistent description of gravity as a non-perturbatively renormalizable quantum field theory. In this framework the gravitational interactions are encoded in a renormalization group flow connecting the quantum gravity regime at trans-Planckian scales to observable low-energy physics. Our proceedings reviews the key elements underlying the predictive power of the construction and summarizes the state-of-the-art in determining its fr...

We study the asymptotic safety conjecture for quantum gravity in the presence of matter fields. A general line of reasoning is put forward explaining why gravitons dominate the high-energy behaviour, largely independently of the matter fields as long as these remain sufficiently weakly coupled. Our considerations are put to work for gravity coupled to Yang-Mills theories with the help of the functional renormalisation group. In an expansion about flat backgrounds, explicit re...

We discuss the conceptual ideas underlying the Asymptotic Safety approach to the nonperturbative renormalization of gravity. By now numerous functional renormalization group studies predict the existence of a suitable nontrivial ultraviolet fixed point. We use an analogy to elementary magnetic systems to uncover the physical mechanism behind the emergence of this fixed point. It is seen to result from the dominance of certain paramagnetic-type interactions over diamagnetic on...

The asymptotic safety scenario of Quantum Einstein Gravity, the quantum field theory of the spacetime metric, is reviewed and it is argued that the theory is likely to be nonperturbatively renormalizable. It is also shown that asymptotic safety implies that spacetime is a fractal in general, with a fractal dimension of 2 on sub-Planckian length scales.

If gravity is asymptotically safe, operators will exhibit anomalous scaling at the ultraviolet fixed point in a way that makes the theory effectively two-dimensional. A number of independent lines of evidence, based on different approaches to quantization, indicate a similar short-distance dimensional reduction. I will review the evidence for this behavior, emphasizing the physical question of what one means by `dimension' in a quantum spacetime, and will discuss possible mec...

The methods of the renormalization group and the $\varepsilon$-expansion are applied to quantum gravity revealing the existence of an asymptotically safe fixed point in spacetime dimensions higher than two. To facilitate this, physical renormalization schemes are exploited where the renormalization group flow equations take a form which is independent of the parameterisation of the physical degrees of freedom (i.e. the gauge fixing condition and the choice of field variables)...

Weinberg's asymptotic safety scenario provides an elegant mechanism to construct a quantum theory of gravity within the framework of quantum field theory based on a non-Gau{\ss}ian fixed point of the renormalization group flow. In this work we report novel evidence for the validity of this scenario, using functional renormalization group techniques to determine the renormalization group flow of the Einstein-Hilbert action supplemented by the two-loop counterterm found by Goro...

In recent years it has emerged that the high energy behavior of gravity could be governed by an ultraviolet non-Gaussian fixed point of the (dimensionless) Newton's constant, whose behavior at high energy is thus {\it antiscreened}. This phenomenon has several astrophysical implications. In particular in this article recent works on renormalization group improved cosmologies based upon a renormalization group trajectory of Quantum Einstein Gravity with realistic parameter val...

In this contribution, we discuss the asymptotic safety scenario for quantum gravity by evaluating the correlation functions of dynamical metric fluctuations. This is done with a functional renormalisation group approach that disentangles dynamical metric fluctuations from the background metric. We detail the derivation of the respective flow equations on space-time manifolds with Euclidean and Lorentzian signatures and discuss the diffeomorphism symmetry constraints on the fl...

Asymptotic Safety provides a mechanism for constructing a consistent and predictive quantum theory of gravity valid on all length scales. Its key ingredient is a non-Gaussian fixed point of the gravitational renormalization group flow which controls the scaling of couplings and correlation functions at high energy. In this work we use a functional renormalization group equation adapted to the ADM-formalism for evaluating the gravitational renormalization group flow on a cosmo...