Dynamical analysis of $R\dfrac{1}{\Box^{2}}R$ cosmology: Impact of   initial conditions and constraints from supernovae
  We discuss the cosmological implications of the $R~\Box^{-2}R$ nonlocal modification to standard gravity. We relax the assumption of special initial conditions in the local formulation of the theory, perform a full phase-space analysis of the system, and show that the late-time cosmology of the model exhibits two distinct evolution paths, on which a large range of values for the present equation of state can be reached. We then compare the general solutions to supernovae data and place constraints on the parameters of the model. In particular, we find that the mass parameter of the theory should be smaller than 1.2 in Hubble units. 
Henrik Nersisyan, Yashar Akrami, Luca Amendola, Tomi S. Koivisto,   Javier Rubio
gr-qc astro-ph.CO hep-th