Equation of state for an interacting holographic dark energy model

TL;DR

This paper explores an interacting holographic dark energy model with cold dark matter, analyzing its effective equations of state and showing it cannot transition from non-phantom to phantom regimes.

Contribution

It introduces a detailed analysis of effective equations of state in an interacting holographic dark energy model, highlighting limitations in transitioning to phantom energy.

Findings

Effective equations of state are negative constants for fixed energy density ratios.

The model cannot describe a transition from $\\omega^{eff}_{\Lambda} \\ge -1$ to less than -1.

Cosmic anti-friction may induce acceleration with $\omega^{eff}_{\Lambda} < -1/3$.

Abstract

We investigate a model of the interacting holographic dark energy with cold dark matter (CDM). If the holographic energy density decays into CDM, we find two types of the effective equation of state. In this case we have to use the effective equations of state ($\omega^{\rm eff}_{\rm \Lambda}$) instead of the equation of state ($\omega_{\rm \Lambda})$. For a fixed ratio of two energy densities, their effective equations of state are given by the same negative constant. Actually, the cosmic anti-friction arisen from the vacuum decay process may induce the acceleration with $\omega^{\rm eff}_{\rm \Lambda}<-1/3$. For a variable ratio, their effective equations of state are slightly different, but they approach the same negative constant in the far future. Consequently, we show that such an interacting holographic energy model cannot accommodate a transition from the dark energy with $\omega^{\rm eff}_{\rm \Lambda}\ge-1$ to the phantom regime with $\omega^{\rm eff}_{\rm \Lambda}<-1$.