Classical and quantum gravity with fractional operators

TL;DR

This paper explores novel quantum gravity theories using fractional operators, analyzing their classical actions, equations of motion, and properties like unitarity and renormalizability, proposing a potentially ghost-free, large-scale modified gravity model.

Contribution

It introduces a new class of perturbative quantum gravity theories based on fractional derivatives, including the construction of classical actions and analysis of their quantum properties.

Findings

Fractional d'Alembertian theories face a trade-off between unitarity and renormalizability.

One theory achieves unitarity and infrared finiteness, offering a ghost-free large-scale gravity model.

Abstract

Following the same steps made for a scalar field in a parallel publication, we propose a class of perturbative theories of quantum gravity based on fractional operators, where the kinetic operator of the graviton is either made of fractional derivatives or a covariant fractional d'Alembertian. The classical action for each theory is constructed and the equations of motion are derived. Unitarity and renormalizability of theories with a fractional d'Alembertian are also considered. We argue that unitarity and power-counting renormalizability never coexist, although in some cases one-loop unitary and finiteness are possible. One of the theories is unitary and infrared-finite and can serve as a ghost-free model with large-scale modifications of general relativity.