Dynamics of coupled phantom and tachyon fields

TL;DR

This work analyzes coupled phantom and tachyon dark-energy models in a flat FLRW universe using dynamical-systems methods. By formulating autonomous equations for multiple phenomenological couplings between dark energy and dark matter, and employing exponential (phantom) and inverse-square (tachyon) potentials, the authors map out stationary points and their stability to identify possible late-time attractors. They find stable accelerating solutions in some phantom-coupled cases, but none yield a scaling, dark-energy–dark-matter ratio of order unity, thereby not solving the cosmic coincidence problem; the tachyon case provides a stable attractor without necessarily achieving a scaling regime. Overall, the results constrain the viability of these simple couplings for addressing the coincidence problem and corroborate prior findings in the literature.

Abstract

In this paper, we apply the dynamical analysis to a coupled phantom field with scaling potential taking particular forms of the coupling (linear and combination of linear), and present phase space analysis. We investigate if there exist late time accelerated scaling attractor that has the ratio of dark energy and dark matter densities of the order one. We observe that the scrutinized couplings cannot alleviate the coincidence problem, however acquire stable late time accelerated solutions. We also discuss coupled tachyon field with inverse square potential assuming linear coupling.

Figures (6)

• Figure 1: The figure shows the phase space trajectories for point (3) of the coupling $Q=\alpha \dot{\rho}_{m}$. The stable fixed point is an attractive node and corresponds to $\alpha=5$ and $\lambda=1$. The black dot represents the stable attractor point.
• Figure 2: This figure represents the phase portrait, evolution of $w_{\phi}$ and $\Omega_{\phi}$ of point (5) for $Q=\alpha \dot{\rho}_{m}$. This is an unstable point and acts as a saddle point that is shown in the left panel for $\alpha=-0.3$ and $\lambda=1.9$. The middle and right panels are plotted for different values of $\alpha$. The solid, dashed, dot-dashed and dotted lines correspond to $\alpha=-1, -2, -3$ and $-5$, respectively. The values of $\lambda$ below horizontal line are not allowed.
• Figure 3: The figure displays the phase space trajectories of Case (2) for $Q=\beta \dot{\rho_{\phi}}$. It is plotted for $\beta=-2$ and $\lambda=1$. The point is stable and behaves as an attractive node.
• Figure 4: The left panel shows the phase portrait of Case (4) for $Q=\beta \dot{\rho_{\phi}}$, and corresponds to $\beta=-2.5$ and $\lambda=1$. The middle and right panels show the evolution of $w_{\phi}$ and $\Omega_{\phi}$ versus $\lambda$ for various values of $\beta$. The solid, dashed, dot-dashed and dotted lines correspond to $\beta=-0.5, -2, -3$ and $-5$, respectively. The values of $\lambda$ below the horizontal line are not accepted. This is a stable point and acts as an attractive node.
• Figure 5: The figure represents the evolution of the phase space trajectories of Case (3) for $Q=\sigma (\dot{\rho}_{m}+ \dot{\rho_{\phi}})$, and is plotted for $\sigma=2$ and $\lambda=1$. The stable point acts as an attractive node, and the black dot designates a stable attractor point.