Coupled Quintessence in a Power-Law Case and the Cosmic Coincidence Problem

Abstract

The problem of the cosmic coincidence is a longstanding puzzle. This conundrum may be solved by introducing a coupling between the two dark sectors. In this Letter, we study a coupled quintessence scenario in which the scalar field evolves in a power law potential and the mass of dark matter particles depends on a power law function of $φ$. It is shown that this scenario has a stable attractor solution and can thus provide a natural solution to the cosmic coincidence problem.

Figures (3)

• Figure 1: The phase plane for $\alpha=11$ and $\beta=4$. The units of $V_\ast$ and $M_\ast$ are in $\rho_{c0}$ and $\rho_{c0}/n_{\chi 0}$, respectively. The three lines correspond to cases $(V_\ast,M_\ast)$ taken to be (0.1,230), (0.2,23) and (0.3,2.3), respectively.
• Figure 2: Top panel: A typical solution for the differential equation (\ref{['eom']}), namely the evolution of the $\phi$ field. The corresponding parameter configuration is: $\alpha=11$, $\beta=4$, $V_\ast=0.1\rho_{c0}$, and $M_\ast=230\rho_{c0}/n_{\chi0}$. Bottom Panel: the evolution of $\phi'$ for the same parameters used in top panel.
• Figure 3: Top panel: The evolution of the relative abundance of different species, expressed as fractions of the critical density. The corresponding model parameters are: $\alpha=11$, $\beta=4$, $V_\ast=0.1\rho_{c0}$, and $M_\ast=230\rho_{c0}/n_{\chi0}$. Bottom panel: Effective equations of state for DE (solid line) and DM (dashed line) for the same parameters used in top panel.