  We consider a class of non-local gravity theories where the Lagrangian is a
function of powers of the inverse d'Alembertian operator acting on the Ricci
scalar. We take an approach in which the non-local Lagrangian is made local by
introducing auxiliary scalar fields, and study the degrees of freedom of the
localized Lagrangian. We find that among the auxiliary scalar fields
introduced, some of them are always ghost-like. That is, in the Einstein frame
they develop a negative kinetic term. Because of this, except for a particular
case already known in the literature, in general, it is not clear how to
quantize these models and how to interpret this theory in the light of standard
field theory.
