Unifying holographic inflation with holographic dark energy: A covariant approach

In the present paper, we use the holographic approach to describe the early-time acceleration and the late-time acceleration eras of our Universe in a unified manner. Such "holographic unification" is found to have a correspondence with various higher curvature cosmological models with or without matter fields. The corresponding holographic cutoffs are determined in terms of the particle horizon and its derivatives, or the future horizon and its derivatives. As a result, the holographic energy density we propose is able to merge various cosmological epochs of the Universe from a holographic point of view. We find the holographic correspondence of several F(R) gravity models, including axion-F(R) gravity models, of several Gauss-Bonnet F(G) models and finally of F(T) models, and in each case we demonstrate that it is possible to describe in a unified way inflation and late-time acceleration in the context of the same holographic model.