Dark energy, inflation and the cosmic coincidence problem

We show that holographic dark energy could explain why the current dark energy density is so small, if there was an inflation with a sufficient expansion in the early universe. It is also suggested that an inflation with the number of e-folds N≃65 may solve the cosmic coincidence problem in this context. Assuming the inflation and the power-law acceleration phase today we obtain approximate formulas for the event horizon size of the universe and dark energy density as functions of time. A simple numerical study exploiting the formula well reproduces the observed evolution of dark energy. This nontrivial match between the theory and the observational data supports both inflation and holographic dark energy models.