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

The quantum theory of General Relativity at low energy exists and is of the form called "effective field theory". In this talk I describe the ideas of effective field theory and its application to General Relativity.

In this proceedings, I will consider quantum aspects of a non-local, infinite-derivative scalar field theory - a ${\it toy \, model}$ depiction of a covariant infinite-derivative, non-local extension of Einstein's general relativity which has previously been shown to be free from ghosts around the Minkowski background. The graviton propagator in this theory gets an exponential suppression making it ${\it asymptotically \, free}$, thus providing strong prospects of resolving v...

We review an approach developed in the last few years by our group in which GR is modified in the infrared, at an effective level, by nonlocal terms associated to a mass scale. We begin by recalling the notion of quantum effective action and its associated nonlocalities, illustrating some of their features with the anomaly-induced effective actions in $D=2$ and $D=4$. We examine conceptual issues of nonlocal theories such as causality, degrees of freedoms and ghosts, stressin...

In the quasistatic regime, generic modifications to gravity can give rise to novel scale-dependence of the gravitational field equations. Crucially, the detectability of the new scale-dependent terms hinges upon the existence of an effective mass scale or length scale at which corrections to General Relativity become relevant. Starting from only a few basic principles, we derive the general form of this scale-dependence. Our method recovers results previously known in the spe...

The bare bones of a theory of quantum gravity are exposed. It may have the potential to solve the cosmological constant problem. Less certain is its behavior in the Newtonian limit.

I discuss a model for quantized gravitation based on the simplicial lattice discretization. It has been studied in some 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 pe...

In this Letter we present a general covariant modified theory of gravity in $D\!=\!4$ space-time dimensions which propagates only the massless graviton and bypasses the Lovelock's theorem. The theory we present is formulated in $D\!>\!4$ dimensions and its action consists of the Einstein-Hilbert term with a cosmological constant, and the Gauss-Bonnet term multiplied by a factor $1/(D\!-\!4)$. The four-dimensional theory is defined as the limit $D\!\to\!4$. In this singular li...

I provide a conceptually-focused presentation of `low-energy quantum gravity' (LEQG), the effective quantum field theory obtained from general relativity and which provides a well-defined theory of quantum gravity at energies well below the Planck scale. I emphasize the extent to which some such theory is required by the abundant observational evidence in astrophysics and cosmology for situations which require a simultaneous treatment of quantum-mechanical and gravitational e...

I briefly summarized some recent work which uses the techniques of effective field theory to make quantum predictions in general relativity. In contrast to conventional expectations, these are in fact well behaved. The leading quantum correction to the interaction of two heavy masses is used as a specific example.

A nonlinear scalar field theory from which an effective metric can be deduced is considered. This metric is shown to be compatible with requirements of general relativity. It is demonstrated that there is a class of solutions which fulfill both the nonlinear field equation as the Einstein equations for this metric.