Gravitational waves in non-local gravity

Understand

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.