Constraints on Gravitational Scaling Dimensions from Non-Local Effective Field Equations

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 question of building a local diff-invariant effective gravitational action for the trace anomaly is reconsidered. General Relativity (GR) combined with the existing action for the trace anomaly is an inconsistent low energy effective field theory. This issue is addressed by extending GR into a certain scalar-tensor theory, which preserves the GR trace anomaly equation, up to higher order corrections. The extension introduces a new mass scale -- assumed to be below the Pla...

This is a review of some of the concepts and results of the effective field theory treatment of quantum general relativity. Included are lessons of low energy quantum gravity, and a discussion of the limits of effective field theory techniques.

A nonrelativistic approach to quantum gravity is studied. At least for weak gravitational fields it should be a valid approximation. Such an approach can be used to point out problems and prospects inherent in a more exact theory of quantum gravity, yet to be discovered. Nonrelativistic quantum gravity, e.g., shows promise for prohibiting black holes altogether (which would eliminate singularities and also solve the black hole information paradox), gives gravitational radiati...

A general introduction is given to what can be predicated about quantum gravity once the lessons from the standard model of particle physics are taken into account. In particular, the effective lagrangian point of view is briefly commented upon .

A four dimensional scalar field theory with quartic and of higher power interactions suffers the triviality issue at the quantum level. This is due to coupling constants that, contrary to the physical expectations, seem to grow without a bound with energy. Since this problem concerns the high energy domain, interaction with a quantum gravitational field may provide natural solution to it. In this paper we address this problem considering a scalar field theory with a general a...

We have recently presented a manifestly local and general coordinate invariant formulation of a nonlocal approach to the cosmological constant problem. In this article, we investigate quantum effects from both matter and gravitational fields in this formulation. In particular, we pay our attention to the gravitational loop effects and show that the effective cosmological constant is radiatively stable even in the presence of the gravitational loop effects in addition to matte...

We identify a simple physical mechanism which is at the heart of Asymptotic Safety in Quantum Einstein Gravity (QEG) according to all available effective average action-based investigations. Upon linearization the gravitational field equations give rise to an inverse propagator for metric fluctuations comprising two pieces: a covariant Laplacian and a curvature dependent potential term. By analogy with elementary magnetic systems they lead to, respectively, dia- and paramagne...

We analyze the cosmological solutions to the recently proposed nonlocal quantum effective action for gravity with a cosmological term. We show that the vacuum energy decays with a slow-roll parameter proportional to the anomalous gravitational dressings.

This article contains a brief pedagogical introduction to various renormalization group related aspects of quantum gravity with an emphasis on the scale dependence of Newton's constant and on black hole physics.