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 ω 1, we obtain a further scalar massive mode with helicity 0 and angular frequency ω 2, whose polarization is transverse. It is a breathing mode, which, at the lowest order of an effective parameter γ, 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.