Gravitational waves in non-local gravity

TL;DR

This paper derives gravitational wave modes in a non-local gravity theory, revealing additional scalar modes and their properties, which differ from standard General Relativity predictions.

Contribution

It introduces a new scalar massive mode in non-local gravity and analyzes its polarization, speed, and classification, expanding understanding beyond standard gravitational wave models.

Findings

Standard tensor modes are present as in GR.

A new scalar breathing mode with transverse polarization is identified.

The theory's gravitational wave modes are classified as type N3 in Petrov classification.

Abstract

We derive gravitational waves in a theory with non-local curvature corrections to the Hilbert-Einstein Lagrangian. In addition to the standard two massless tensor modes, with plus and cross polarizations, helicity 2 and angular frequency $\omega_{1}$, we obtain a further scalar massive mode with helicity 0 and angular frequency $\omega_{2}$, whose polarization is transverse. It is a breathing mode, which, at the lowest order of an effective parameter $\gamma$, presents a speed difference between nearly null and null plane waves. Finally, the quasi-Lorentz $E(2)$-invariant class for the non-local gravity is type $N_{3}$, according to the Petrov classification. This means that the presence (or absence) of gravitational wave modes is observer-independent.