Causality Problem in a Holographic Dark Energy Model

TL;DR

This paper addresses causality and circular reasoning issues in holographic dark energy models, proposing a way to resolve these problems by properly defining boundary conditions and initial data.

Contribution

It clarifies the causality problem in holographic dark energy and demonstrates that the circular logic can be avoided through proper initial value formulation.

Findings

No causality violation with proper boundary conditions

Circular logic reduces to an initial value problem

Root of the problem identified in boundary condition formulation

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 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 problem from causal equation of motion as a boundary condition, which can be determined from the initial data of the universe. We show that there is no violation of causality if it is defined appropriately and the circular logic problem can be reduced to an initial value problem.