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

TL;DR

This paper investigates the cosmological effects of a nonlocal gravity modification involving $R\Box^{-2} R$, analyzing initial conditions, phase space, and observational constraints from supernovae data.

Contribution

It provides a comprehensive phase-space analysis of the $R\Box^{-2} R$ model and derives observational constraints on its parameters.

Findings

Late-time cosmology has two distinct evolution paths.

The model's mass parameter must be less than 1.2 in Hubble units.

Supernovae data constrain the model's parameters.

Abstract

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.