Thermodynamics second law and $ω=-1$ crossing(s) in interacting holographic dark energy model

TL;DR

This paper investigates whether the phantom divide crossing at $\omega = -1$ can occur in an interacting holographic dark energy model while respecting the thermodynamics second law. By modeling the IR cutoff $L$ as a linear combination of the future event horizon and particle horizon and including a dark matter–dark energy interaction $Q = (\lambda_m \rho_m + \lambda_D \rho_D) H$, the authors derive relations for the cosmic equation of state in terms of $\Omega_D$ and analyze conditions for $\omega = -1$ crossing. They show that $\omega = -1$ crossing may entail one or two transitions (quintessence to phantom and phantom to quintessence), with the latter serving to avoid the big rip, and derive necessary algebraic and Sturm-theoretical conditions for the existence of real roots in $(0,1)$. They illustrate parameter regions that permit two transitions and discuss implications for the Hubble evolution and coincidence problem. The work links holographic dark energy phenomenology with thermodynamic constraints to provide a framework for phantom divide crossing without singularities.

Abstract

By the assumption that the thermodynamics second law is valid, we study the possibility of $ω=-1$ crossing in interacting holographic dark energy model. Depending on the choice of the horizon and the interaction, the transition from quintessence to phantom regime and subsequently from phantom to quintessence phase may be possible. The second transition avoids the big rip singularity. We compute the dark energy density at transition time and show that by choosing appropriate parameters we can alleviate the coincidence problem.

Figures (1)

• Figure 1: $\omega+1$ as a function of $u$, for $\{\beta=0$, $\alpha=1$, $c=1$, $\lambda_D=3.9$, $\lambda_m=2.5\}$