Covariant generalized holographic dark energy and accelerating universe

We propose the generalized holographic dark energy model where the infrared cutoff is identified with the combination of the FRW universe parameters: the Hubble rate, particle and future horizons, cosmological constant, the universe lifetime (if finite) and their derivatives. It is demonstrated that with the corresponding choice of the cutoff one can map such holographic dark energy to modified gravity or gravity with a general fluid. Explicitly, F(R) gravity and the general perfect fluid are worked out in detail and the corresponding infrared cutoff is found. Using this correspondence, we get realistic inflation or viable dark energy or a unified inflationary-dark energy universe in terms of covariant holographic dark energy.