Causality problem in a holographic-dark-energy model

Abstract

In the model of holographic dark energy, there is a notorious problem of circular reasoning between the introduction of future event horizon and the accelerating expansion of the universe. We examine the problem after dividing it into two parts, the causality problem of the equation of motion and the circular logic on the use of the future event horizon. We specify and isolate the root of the two problems as a boundary condition from the causal equation of motion, which can be determined from the initial data of the universe. We show that the causality will be kept if we define it based on our recognizability and the circular-logic problem can be reduced to imposing an initial condition. We additionally find that the model constant of the holographic dark energy is close to unity from the present data of the universe.