On nonlocally interacting metrics, and a simple proposal for cosmic acceleration

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.