Quantum Loops in Non-Local Gravity

We employ the curvature expansion of the quantum effective action for gravity-matter systems to construct graviton-mediated scattering amplitudes for non-minimally coupled scalar fields in a Minkowski background. By design, the formalism parameterises all quantum corrections to these processes and is manifestly gauge-invariant. The conditions resulting from UV-finiteness, unitarity, and causality are analysed in detail and it is shown by explicit construction that the quantum...

We study the one-loop effective action for gravity in a cosmological setup to determine possible cosmological effects of quantum corrections to Einstein theory. By considering the effect of the universal non-local terms in a toy model, we show that they can play an important role in the very early universe. We find that during inflation, the non-local terms are significant, leading to deviations from the standard inflationary expansion.

We study perturbative noncommutative quantum gravity by expanding the gravitational field about a fixed classical background. A calculation of the one loop gravitational self-energy graph reveals that only the non-planar graviton loops are damped by oscillating internal momentum dependent factors. The noncommutative quantum gravity perturbation theory is not renormalizable beyond one loop for matter-free gravity and all loops for matter interactions. Comments are made about t...

The purpose of these lectures is to discuss in some detail a new, non-perturbative approach to quantum gravity. I would like to present the basic ideas, outline the key results that have been obtained so far and indicate where we are headed and what the hopes are. The audience at this summer school had a diverse background; many came from high energy physics, some from mathematical physics and the rest from general relativity. Therefore, I have tried to keep the technicalitie...

In this paper we will study Lorentz-invariant, infinite derivative quantum field theories, where infinite derivatives give rise to non-local interactions at the energy scale $M_s$, beyond the Standard Model. We will study a specific class, where there are no it new dynamical degrees of freedom other than the original ones of the corresponding local theory. We will show that the Green functions are modified by a non-local extra term that is responsible for acausal effects, whi...

We derive the N=1 supersymmetric extension for a class of weakly nonlocal four dimensional gravitational theories.The construction is explicitly done in the superspace and the tree-level perturbative unitarity is explicitly proved both in the superfield formalism and in field components. For the minimal nonlocal supergravity the spectrum is the same as in the local theory and in particular it is ghost-free. The supersymmetric extension of the super-renormalizable Starobinsky ...

It was recently found that there are classes of nonlocal gravity theories that are free of ghosts and singularities in their Newtonian limit [PRL, 108 (2012), 031101]. In these proceedings, a detailed and pedagogical derivation of a main result, the flat space propagator for an arbitrary covariant metric theory of gravitation, is presented. The result is applied to analyse f(R) models, Gauss-Bonnet theory, Weyl-squared gravity and the potentially asymptotically free nonlocal ...

This is a review paper invited by the journal "Classical ad Quantum Gravity" for a "Cluster Issue" on approaches to quantum gravity. I give a synthetic presentation of loop gravity. I spell-out the aims of the theory and compare the results obtained with the initial hopes that motivated the early interest in this research direction. I give my own perspective on the status of the program and attempt of a critical evaluation of its successes and limits.

We study two--loop renormalization in $(2+\epsilon)$--dimensional quantum gravity. As a first step towards the full calculation, we concentrate on the divergences which are proportional to the number of matter fields. We calculate the $\beta$ functions and show how the nonlocal divergences as well as the infrared divergences cancel among the diagrams. Although the formalism includes a subtlety concerning the general covariance due to the dynamics of the conformal mode, we fin...

Nonlocal gravity has been shown to provide a phenomenologically viable infrared modification of GR. A natural question is whether the required nonlocality can emerge from perturbative quantum loop corrections due to light particles. We show that this is not the case. For the value of the mass scale of the non-local models required by cosmology, the perturbative form factors obtained from the loop corrections, in the present cosmological epoch, are in the regime where they are...