The 1.5 post-Newtonian radiative quadrupole moment in the context of a nonlocal field theory of gravity

We recently suggested a nonlocal modification of Einstein’s field equations in which Newton’s constant $G$ was promoted to a covariant differential operator $G_{\mathrm{\Lambda }}({\mathrm{\square }}_g)$. The latter contains two independent contributions, which operate respectively in the infrared (IR) and ultraviolet (UV) energy regimes. In the light of the recent direct gravitational radiation measurements we aim to determine the UV-modified 1.5 post-Newtonian radiative quadrupole moment of a generic $n$-body system. We eventually use these initial results in the particular context of a binary system and observe that in the limit vanishing UV parameters we precisely recover the corresponding general relativistic results. Moreover we observe that the leading order deviation of the UV-modified radiative quadrupole moment numerically coincides with findings obtained in the framework of calculations performed previously in the context of possible deviations of the perihelion precession of Mercury.