Cosmology with Interaction between Phantom Dark Energy and Dark Matter and the Coincidence Problem

TL;DR

The paper analyzes a flat FRW cosmology in which phantom dark energy interacts with dark matter via a phenomenological coupling term $δ H ρ_m$, aiming to address the coincidence problem. It treats two principal setups: a constant equation-of-state $ω_e$ and a constant coupling $δ$, deriving exact scaling relations for energy densities and the Hubble parameter, and quantifying how the interaction alters cosmic evolution, the total lifetime, and the duration of the coincidence epoch. Key findings show that the interaction can substantially extend the phantom-dominated lifetime and raise the fraction of time during which $ρ_e$ and $ρ_m$ are comparable, with values like $f ≈ 0.45$ for particular parameter choices. The results underscore the importance of combining SNIa, CMB, and LSS constraints to bound $δ$ and $ω_e$, and suggest that dark-sector coupling can alleviate the coincidence problem within phantom cosmologies.

Abstract

We study a cosmological model in which phantom dark energy is coupled to dark matter by phenomenologically introducing a coupled term to the equations of motion of dark energy and dark matter. This term is parameterized by a dimensionless coupling function $δ$, Hubble parameter and the energy density of dark matter, and it describes an energy flow between the dark energy and dark matter. We discuss two cases: one is the case where the equation-of-state $ω_e$ of the dark energy is a constant; the other is that the dimensionless coupling function $δ$ is a constant. We investigate the effect of the interaction on the evolution of the universe, the total lifetime of the universe, and the ratio of the period when the universe is in the coincidence state to its total lifetime. It turns out that the interaction will produce significant deviation from the case without the interaction.

Figures (14)

• Figure 1: The deceleration parameter $q$ versus the red shift $z$ for the case of $\Omega_{e,0}=0.72$ and $\omega_e=-1.5$. Three curves from top to bottom correspond to the cases $\xi=5.5$, $4.5$ and $3$, respectively. Note that the case of $\xi =4.5 = -3 \omega_e$ is just the case without interaction.
• Figure 2: The deceleration parameter $q$ versus the red shift $z$ for the case of $\Omega_{e,0}=0.72$ and $\omega_e=-1.3$. Three curves from top to bottom correspond to the cases $\xi=5.5$, $4.5$ and $3$, respectively.
• Figure 3: The deceleration parameter $q$ versus the red shift $z$ for the case of $\Omega_{e,0}=0.72$ and $\omega_e=-1.1$. Three curves from top to bottom correspond to the cases $\xi=5.5$, $4.5$ and $3$, respectively.
• Figure 4: The ratio $g$ of total lifetimes versus the parameter $\xi=x$ for the case of $\Omega_{e,0}=0.72$. Three curves from bottom to top correspond to the cases $\omega_e=-1.5$, $-1.3$ and $-1.1$, respectively.
• Figure 5: The ratio $g$ of total lifetimes versus the parameters $\xi=x$ and $\omega_e$ in the case of $\Omega_{e,0}=0.72$.