| dc.description.abstract | This work is a continuation of [arXiv:1811.04647], which computed the energy-momentum flux in $f[R/Box]$ nonlocal gravity model, where $R$ is the Ricci Scalar and $Box$ is the d′Alembertian operator. In (3+1)D Minkowski spacetime, the gravitational energy-momentum flux is supposed to scale at most $1/r^{2}$ as $r
ightarrow infty$, where $r$ is the distance from the observer to the source. To examine the energy flux, we need to perturb the equation of motions from the nonlocal models up to quadratic order in metric perturbation. In this work, we investigate some nonlocal gravity models likewise the second model of the Deser-Woodard, VAAS model, and ABN model. We find that the VAAS and ABN models do not have an exact solution in Minkowski background. So, we work both models in Fermi-Normal-Coordinates (FNC) cosmological background that consist of flat spacetime and corrections in terms of the distance from the free-falling observer to the source. We obtain the Deser-Woodard II model that corresponds to $f[Y]$, where $Y$ consists of $R/Box$, can avoid the divergent flux by setting $f′[0]=0$, similar in the case from the first model of Deser-Woodard. However, the nonlocal gravity $m^{2}(R/Box)$, called VAAS and $M^{4}(R/Box^{2})$, called ABN suffers from the divergent flux because the energy-momentum flux scale as $r^{0}$ and $r^{2}$ respectively. From our works so far, the nonlocal gravity needs deeper understanding to construct the model that yields a sensible gravitational radiation flux comparable to that of Einstein′s General Relativity. | en_US |