Dynamical analysis of $R\dfrac{1}{\Box^{2}}R$ cosmology: Impact of initial conditions and constraints from supernovae

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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.