Gravitational radiation in higher order non-local gravity

Abstract

In this paper we examine gravitational radiation in higher order non-local gravity described by the non-local gravitational Lagrangian density Lg = R + n h=1 a h R −h R. This non-local theory of gravitation always exhibits the tensor transverse gravitational radiation for k 2 1 = 0, corresponding to the angular frequency ω1, composed of two standard (+) and (×) polarization modes, massless and of helicity 2. Furthermore, it shows, under suitable constraint and n ≥ 2, an additional massive transverse scalar gravitational radiation with helicity 0. It is composed of n − 1 modes associated to n − 1 angular frequencies ω2, . . . , ωn, each of which of breathing polarization (b) to lowest order in γ, a parameter that takes into account the difference in speed between the slightly massive wave and the massless one. Thanks to NP formalism, we find that the E(2) class of non-local gravitational waves is N3, according Petrov classification, where the presence or absence of all modes are observer independent. Also, the scalar radiation is forbidden for n = 1 and n = 2 cases, when some conditions are satisfied. Finally, in −1 gravity where n = 1, a possible degenerate case with a continuous infinity of transverse massive scalar breathing modes appears under a particular constraint, which reproduces in two-dimensional spacetime the Polyakov effective action.