Gravitational waves in non-local gravity

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.

22 pages, accepted for publication in Classical and Quantum Gravity

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