Divergent Energy-Momentum Fluxes In Nonlocal Gravity Models

TL;DR

This paper investigates the energy-momentum fluxes of gravitational waves in three nonlocal gravity models, revealing divergences that challenge their physical viability on large scales.

Contribution

It provides the first detailed analysis of second order perturbations and gravitational wave fluxes in the DWII, VAAS, and ABN nonlocal gravity models.

Findings

DWII model has a divergent flux unless the first derivative of its distortion function at the origin is zero.

ABN model exhibits a divergent flux due to its momentum density scaling as r^2.

VAAS model's momentum density scales as r, leading to non-well-defined gravitational wave energies.

Abstract

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 $r \rightarrow \infty$ 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.