Acausality in Nonlocal Gravity Theory
  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.
