Divergent energy-momentum fluxes in nonlocal gravity models

We analyze the second order perturbations of the Deser-Woodard II (DWII), Vardanyan-Akrami-Amendola-Silvestri (VAAS), and Amendola-Burzilla-Nersisyan (ABN) nonlocal gravity models in an attempt to extract their associated gravitational wave energy-momentum fluxes. In Minkowski spacetime, the gravitational spatial momentum density is supposed to scale at most as $1/{r}^{2}$, in the $r\ensuremath{\rightarrow}\ensuremath{\infty}$ limit, where $r$ is the observer-source spatial distance. The DWII model has a divergent flux because its momentum density goes as $1/r$; though this can be avoided when we set to zero the first derivative of its distortion function at the origin. Meanwhile, the ABN model also suffers from a divergent flux because its momentum density goes as ${r}^{2}$. The momentum density from the VAAS model was computed on a cosmological background expressed in a Fermi-Normal-Coordinate system, and was found to scale as $r$. For generic parameters, therefore, none of these three dark energy models appear to yield well-defined gravitational wave energies, as a result of their nonlocal gravitational self-interactions.