Modified non-local-F(R) gravity as the key for the inflation and dark energy

TL;DR

The paper addresses the challenge of explaining both early-time inflation and late-time cosmic acceleration within a single modified-gravity framework while respecting local gravity tests. It develops a non-local gravity model that can be localized to a scalar-tensor form with auxiliary fields and shows how de Sitter and power-law solutions can realize inflation and phantom/quintessence regimes; it also demonstrates that coupling a non-local term to an F(R) term enables flexible unification scenarios. The authors present explicit constructions with an exponential non-local function and with specific F(R) forms (e.g., β R^2 and Hu-Sawicki) to realize a sequence of epochs: inflation, radiation/matter domination, and dark energy, while keeping Newtonian corrections small and avoiding ghostly instabilities. Overall, the work proposes a viable, testable route to unify the universe’s expansion history within non-local gravity and motivates further analysis of perturbations and observational constraints.

Abstract

We consider FRW cosmology in non-local modified gravity. Its local scalar-tensor formulation is developed. It is explicitly demonstrated that such theory may lead to the unification of early-time inflation with late-time cosmic acceleration. The quintessence or phantom era may emerge for specific form of the action. The coupled non-local-F(R) gravity is also investigated. It is shown that such theory being consistent with Solar System tests may lead to the known universe history sequence: inflation, radiation/matter dominance and dark epoch.