Super-renormalizable Higher-Derivative Quantum Gravity

TL;DR

This paper proposes a super-renormalizable, ghost-free higher-derivative quantum gravity theory using entire functions to avoid unitarity issues, and demonstrates its improved regularity and divergence properties.

Contribution

It introduces an infinite-derivative extension of gravity with entire functions, achieving super-renormalizability and ghost-free behavior without new poles.

Findings

The theory is super-renormalizable, finite from two loops upwards.

The modified propagator ensures a regular gravitational potential at r=0.

The model avoids ghosts by using entire functions without new poles.

Abstract

In this paper we study perturbatively an extension of the Stelle higher derivative gravity involving an infinite number of derivative terms. We know that the usual quadratic action is renormalizable but is not unitary because of the presence of a ghost in the theory (pole with negative residue in the propagator). The new theory is instead ghost-free since an entire function (or form factor) is introduced in the model without involving new poles in the propagator. The local high derivative theory is recovered expanding the entire functions to the lowest order in the mass scale of the theory. Any truncation of the entire function gives rise to unitarity violation. The theory is divergent at one loop and finite from two loops upwards: the theory is then super-renormalizable. Using the modified graviton propagator, we demonstrate the regularity of the gravitational potential in r=0.