Acausality in Nonlocal Gravity Theory

TL;DR

This paper analyzes a nonlocal gravity theory, revealing that it inherently contains acausality issues due to advanced Green's functions, leading to divergences unless the universe evolves to specific future states.

Contribution

It demonstrates that nonlocal gravity models with linear modifications inevitably face acausality problems that cannot be resolved by modifying the nonlocal terms.

Findings

Equations of motion include advanced Green's functions.

Acausality causes divergences unless universe reaches radiation or Minkowski state.

Acausality cannot be eliminated by any choice of nonlocal functions.

Abstract

We investigate the nonlocal gravity theory by deriving nonlocal equations of motion using the traditional variation principle in a homogeneous background. We focus on a class of models with a linear nonlocal modification term in the action. It is found that the resulting equations of motion contain the advanced Green's function, implying that there is an acausality problem. As a consequence, a divergence arises in the solutions due to contributions from the future infinity unless the Universe will go back to the radiation dominated era or become the Minkowski spacetime in the future. We also discuss the relation between the original nonlocal equations and its biscalar-tensor representation and identify the auxiliary fields with the corresponding original nonlocal terms. Finally, we show that the acusality problem cannot be avoided by any function of nonlocal terms in the action.