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

We review the status of a certain (infinite) class of four-dimensional generally covariant theories propagating two degrees of freedom that are formulated without any direct mention of the metric. General relativity itself (in its Plebanski formulation) belongs to the class, so these theories are examples of modified gravity. We summarize the current understanding of the nature of the modification, of the renormalizability properties of these theories, of their coupling to ma...

I show, on the most elementary grounds, its classical ultraviolet catastrophe, that even source-free General Relativity must be quantized, despite some eminent opinions to the contrary, an original result involving some rather tricky subtleties.

We highlight the fact that the lack of scale invariance in the gravitational field equations of General Relativity results from the underlying assumption that the appropriate scale for the gravitational force should be linked to the atomic scale. We show that many of the problems associated with cosmology and quantum gravity follow directly from this assumption. An alternative scale invariant paradigm is proposed, in which the appropriate scale for General Relativity takes th...

One of the great challenges for 21st century physics is to quantize gravity and generate a theory that will unify gravity with the other three fundamental forces of nature. This paper takes the (heretical) point of view that gravity may be an inherently classical, i.e., nonquantum, phenomenon and investigates the experimental consequences of such a model. At present there is no experimental evidence of the quantum nature of gravity and the liklihood of definitive tests in the...

We point out the idea that, at small scales, gravity can be described by the standard degrees of freedom of general relativity, plus a scalar particle and a degree of freedom of a new type: the fakeon. This possibility leads to fundamental implications in understanding gravitational force at quantum level as well as phenomenological consequences in the corresponding classical theory.

A model for quantized gravitation based on the simplicial lattice discretization is studied in detail using a comprehensive finite size scaling analysis combined with renormalization group methods. The results are consistent with a value for the universal critical exponent for gravitation $\nu=1/3$, and suggest a simple relationship between Newton's constant, the gravitational correlation length and the observable average space-time curvature. Some perhaps testable phenomenol...

Effective equations are often useful to extract physical information from quantum theories without having to face all technical and conceptual difficulties. One can then describe aspects of the quantum system by equations of classical type, which correct the classical equations by modified coefficients and higher derivative terms. In gravity, for instance, one expects terms with higher powers of curvature. Such higher derivative formulations are discussed here with an emphasi...

This article provides a cartoon of the quantization of General Relativity using the ideas of effective field theory. These ideas underpin the use of General Relativity as a theory from which precise predictions are possible, since they show why quantum corrections to standard classical calculations are small. Quantum corrections can be computed controllably provided they are made for the weakly-curved geometries associated with precision tests of General Relativity, such as w...

We examine the role of consistency with causality and quantum mechanics in determining the properties of gravitation. We begin by examining two different classes of interacting theories of massless spin 2 particles -- gravitons. One involves coupling the graviton with the lowest number of derivatives to matter, the other involves coupling the graviton with higher derivatives to matter, making use of the linearized Riemann tensor. The first class requires an infinite tower of ...

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.