Gravitational radiation in higher order non-local gravity

TL;DR

This paper investigates gravitational waves in higher order non-local gravity theories, revealing the existence of massless tensor modes and additional massive scalar modes, with implications for wave polarization and classification.

Contribution

It provides a detailed analysis of gravitational radiation in non-local gravity, identifying conditions for various polarization modes and classifying wave types using NP formalism.

Findings

Existence of massless tensor modes with standard polarizations.

Presence of additional massive scalar modes for n ≥ 2.

Scalar radiation is absent for n=1 and n=2 under certain conditions.

Abstract

In this paper we examine gravitational radiation in higher order non-local gravity described by the non-local gravitational Lagrangian density $\mathcal{L}_{g}=R+\sum_{h=1}^{n}a_{h}R\Box^{-h}R$. This non-local theory of gravitation always exhibits the tensor transverse gravitational radiation for $k_{1}^{2}=0$, corresponding to the angular frequency $\omega_{1}$, composed of two standard $(+)$ and $(\times)$ polarization modes, massless and of helicity 2. Furthermore, it shows, under suitable constraint and $n\geq 2$, an additional massive transverse scalar gravitational radiation with helicity 0. It is composed of $n-1$ modes associated to $n-1$ angular frequencies $\omega_{2},\ldots,\omega_{n}$, each of which of breathing polarization $(b)$ to lowest order in $\gamma$, 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 $N_{3}$, 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 $\Box^{-1}$ 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.