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

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...

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 .

General relativity and quantum mechanics are perhaps the two most successful theories of the XXth century. Despite their impressive accurate predictions, they are both valid at their own scales and do not seem to be expressible using the same framework. It is commonly accepted that in order to create a consistent theory of both quantum mechanics and gravity, it is required to quantize the gravitational field. In the present paper, another path is taken on which the Einstein f...

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...

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...

The existence of a new fundamental scale may lead to modified dispersion relations for particles at high energies. Such modifications seem to be realized with the Planck scale in certain descriptions of quantum gravity. We apply effective field theory to this problem and identify dimension 5 operators that would lead to cubic modifications of dispersion relations for Standard Model particles. We also discuss other issues related to this approach including various experimental...

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...

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...

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.

Several approaches to quantum gravity (including the model of superplastic vacuum; Diakonov tetrads emerging as the bilinear combinations of the fermionis fields; $BF$-theories of gravity; and effective acoustic metric) suggest that in general relativity the metric must have dimension 2, i.e. $[g_{\mu\nu}]=1/[L]^2$, irrespective of the dimension of spacetime. This leads to the "dimensionless physics" discussed in the review paper G.E. Volovik, Dimensionless physics, JETP 132,...