Interacting Generalized Chaplygin-Jacobi gas: Thermodynamics approach

TL;DR

This work proposes an interacting dark-energy model in which the GCJG (Generalized Chaplygin Jacobi gas) acts as a unified dark energy component and exchanges energy with pressureless dark matter via a linear coupling $Q = 3 H b^2 \rho_x$. The authors derive exact analytic evolutions for the dark-energy and dark-matter densities, with $\rho_x(a,\mathcal{k})$ expressed in closed form for $\mathcal{k}=1$ and via arctanh and Appell hypergeometric functions for $0\le \mathcal{k}<1$, and they analyze the thermodynamic viability of the model. They find positive temperatures for both components, entropy production consistent with the second law, and a phantom crossing for the effective dark-energy EoS in the past, along with a late-time phase transition in the dark-energy sector; the dark-matter sector shows small deviations from perfect cold dark matter. The results suggest potential implications for the $H_0$ tension and DESI-era hints, and they motivate further work on perturbations, observational constraints, and connections to scalar-field or modified-gravity frameworks.

Abstract

This work investigates a cosmological model featuring an interaction between dark energy and dark matter, where the dark energy component is described by the Generalized Chaplygin-Jacobi gas (GCJG). In this study, we establish a system in which the GCJG and a pressureless dark matter fluid exchange energy via a linear interaction term, $Q \propto ρ_x$, being $ρ_{x}$ the dark energy density. By solving the conservation equations, we derive analytical expressions for the evolution of the dark energy and dark matter densities. The thermodynamic properties of this interacting system are then thoroughly analyzed. The thermodynamic analysis reveals that both dark components maintain positive temperatures, ensuring stability. Notably, the dark energy component transitions to a phantom regime in the past, a feature of interest for recent cosmological observations, without violating thermodynamic principles. The total entropy production is shown to be in agreement with the second law of thermodynamics. Furthermore, an analysis of the specific heats suggests that while the dark matter sector remains thermodynamically stable, the dark energy sector undergoes a late-time phase transition, consistent with its entering into the phantom domain at effective level.

Figures (8)

• Figure 1: The $z$-profiles of the density functions $\rho_x$ and $\rho_m$, plotted for $\rho_{x0} = 0.7$, $\rho_{m0}=0.3$, $B=0.01$, $b=0.2$ and $\alpha=0.1$.
• Figure 2: The $z$-profile for the $Q$-term, $Q = 3 H b^2 \rho_x$.
• Figure 3: Hubble parameter as function of the redshift using the energy densities $\rho_{m}$ and $\rho_{x}$. We have considered the Planck 2018 results for the values of the cosmological parameters involved 2020.
• Figure 4: Temperatures of the dark sector as function of the cosmological redshift.
• Figure 5: Effective parameter of state for the matter and the dark sector as functions of the cosmological redshift.