Nonlocal gravity with worldline inversion symmetry

TL;DR

This paper develops a nonlocal quadratic curvature gravity theory respecting worldline inversion symmetry, resulting in a ghost-free model that smooths out singularities while maintaining only the massless graviton.

Contribution

It introduces a novel nonlocal gravity model with worldline inversion symmetry, ensuring ghost-freedom and singularity resolution without extra degrees of freedom.

Findings

The theory is ghost-free despite higher derivatives.

Point-like singularities are smoothed out in the linear regime.

The model maintains only the massless spin-2 graviton.

Abstract

We construct a quadratic curvature theory of gravity whose graviton propagator around the Minkowski background respects wordline inversion symmetry, the particle approximation to modular invariance in string theory. This symmetry automatically yields a corresponding gravitational theory that is nonlocal, with the action containing infinite order differential operators. As a consequence, despite being a higher order derivative theory, it is ghost-free and has no degrees of freedom besides the massless spin-$2$ graviton of Einstein's general relativity. By working in the linearised regime we show that the point-like singularities that afflict the (local) Einstein's theory are smeared out.