Non-perturbative spectrum of non-local gravity

Gianluca Calcagni,Leonardo Modesto,Giuseppe Nardelli

doi:10.1016/j.physletb.2019.06.043

Abstract

We investigate the non-perturbative degrees of freedom of a class of weakly non-local gravitational theories that have been proposed as an ultraviolet completion of general relativity. At the perturbative level, it is known that the degrees of freedom of non-local gravity are the same of the Einstein–Hilbert theory around any maximally symmetric spacetime. We prove that, at the non-perturbative level, the degrees of freedom are actually eight in four dimensions, contrary to what one might guess on the basis of the “infinite number of derivatives” present in the action. It is shown that six of these degrees of freedom do not propagate on Minkowski spacetime, but they might play a role at large scales on curved backgrounds. We also propose a criterion to select the form factor almost uniquely.

Highlights

A quantum theory of gravity [1,2,3] should be able to solve, or say something constructive about, some problems left open in general relativity, such as the singularity problem, the cosmological constant problem, and the mystery surrounding the birth and first stage of development of the Universe
The conclusion is that the equations of motion (EOM) can be expressed in terms of the kernels K and G living in the space of form factors and the Green function G (x, y)
The diffusion-equation method revealed that a string-motivated non-local scalar field theory with exponential operators has a finite number of initial conditions and nonperturbative degrees of freedom [37]

Summary

Introduction

A quantum theory of gravity [1,2,3] should be able to solve, or say something constructive about, some problems left open in general relativity, such as the singularity problem (there exist spacetime points where the laws of physics break down, as in the big bang at the beginning of the Universe or inside black holes), the cosmological constant problem (two thirds of the content of our patch of the cosmos is made of a “dark energy” component not adequately described by general relativity or particle physics), and the mystery surrounding the birth and first stage of development of the Universe (the actual origin of the inflaton is unknown). Theory may resolve the big bang [17,18,19,20,21,22,23,24,25] and black-hole singularities [26,27,28,29,30,31], and its cosmological solutions may unravel interesting bottom-up scenarios in the early universe (inflation) and at late times (dark energy) These encouraging features are accompanied by a number of appalling gaps of knowledge on basic questions on the classical theory, such as how to find solutions of the dynamics and whether they match the singularity-free geometries found when linearizing the equations of motion. The proof is self-contained and may be skipped by the reader interested only in the physical consequences of the theory, which are discussed above and in the final section

Brief overview of non-local quantum gravity

Non-local dynamics in terms of kernels

Master equations

Initial conditions for special form factors

Degrees of freedom

Applications and conclusions