Gravitational waves in non-local gravity

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