  We propose a simple, nonlocal modification to general relativity (GR) on
large scales, which provides a model of late-time cosmic acceleration in the
absence of the cosmological constant and with the same number of free
parameters as in standard cosmology. The model is motivated by adding to the
gravity sector an extra spin-2 field interacting nonlocally with the physical
metric coupled to matter. The form of the nonlocal interaction is inspired by
the simplest form of the Deser-Woodard (DW) model, $\alpha R\frac{1}{\Box}R$,
with one of the Ricci scalars being replaced by a constant $m^{2}$, and gravity
is therefore modified in the infrared by adding a simple term of the form
$m^2\frac{1}{\Box}R$ to the Einstein-Hilbert term. We study cosmic expansion
histories, and demonstrate that the new model can provide background expansions
consistent with observations if $m$ is of the order of the Hubble expansion
rate today, in contrast to the simple DW model with no viable cosmology. The
model is best fit by $w_0\sim-1.075$ and $w_a\sim0.045$. We also compare the
cosmology of the model to that of Maggiore and Mancarella (MM),
$m^2R\frac{1}{\Box^2}R$, and demonstrate that the viable cosmic histories
follow the standard-model evolution more closely compared to the MM model. We
further demonstrate that the proposed model possesses the same number of
physical degrees of freedom as in GR. Finally, we discuss the appearance of
ghosts in the local formulation of the model, and argue that they are
unphysical and harmless to the theory, keeping the physical degrees of freedom
healthy.
