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 cut-offs 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.