Classical and quantum nonlocal gravity

TL;DR

This paper explores how nonlocal modifications to gravity can address fundamental issues like renormalizability and unitarity, potentially resolving singularities and eliminating ghost modes in quantum gravity theories.

Contribution

It demonstrates how nonlocal operators can make gravity theories both renormalizable and ghost-free, improving upon Stelle's quadratic gravity.

Findings

Nonlocal operators can remove Ostrogradski ghosts.

Nonlocality can preserve unitarity in quantum gravity.

Exponential and polynomial form factors enhance renormalizability.

Abstract

This chapter of the Handbook of Quantum Gravity aims to illustrate how nonlocality can be implemented in field theories, as well as the manner it solves fundamental difficulties of gravitational theories. We review Stelle's quadratic gravity, which achieves multiplicative renormalizability successfully to remove quantum divergences by modifying the Einstein's action but at the price of breaking the unitarity of the theory and introducing Ostrogradski's ghosts. Utilizing nonlocal operators, one is able not only to make the theory renormalizable, but also to get rid of these ghost modes that arise from higher derivatives. We start this analysis by reviewing the classical scalar field theory and highlighting how to deal with this new kind of nonlocal operators. Subsequently, we generalize these results to classical nonlocal gravity and, via the equations of motion, we derive significant results about the stable vacuum solutions of the theory. Furthermore, we discuss the way nonlocality could potentially solve the singularity problem of Einstein's gravity. In the final part, we examine how nonlocality induced by exponential and asymptotically polynomial form factors preserves unitarity and improves the renormalizability of the theory.