| Summary: | We consider non-local Integral Kernel Theories of Gravity in a homogeneous and isotropic universe background as a possible scenario to drive the cosmic history. In particular, we investigate the cosmological properties of a gravitational action containing the inverse d'Alembert operator of the Ricci scalar proposed to improve Einstein's gravity at both high and low-energy regimes. In particular, the dynamics of a physically motivated non-local exponential coupling is analyzed in detail by recasting the cosmological equations as an autonomous system of first-order differential equations with dimensionless variables. Consequently, we study the phase-space domain and its critical points, investigating their stability and main properties. In particular, saddle points and late-time cosmological attractors are discussed in terms of the free parameters of the model. Finally, we discuss the main physical consequences of our approach in view of dark energy behavior and the ΛCDM model.
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