Dynamics of dark energy with a coupling to dark matter

TL;DR

Investigates the background evolution of a universe with exponential quintessence and a dark-sector coupling to address the coincidence problem. It analyzes three coupling forms, with model (III) $Q=\\Gamma \\rho_c$ introducing a local, constant-rate transfer and a 3D phase space. Models (I) and (II) admit accelerated scaling attractors in some parameter ranges but face issues with a realistic matter era; Model (III) yields a late-time attractor with DE domination ($\\Omega_{c*}=0$, $\\Omega_{\\varphi*}=1$) for $\\gamma>0$, akin to $\\Lambda$CDM, yet lacks an accelerated scaling. The analysis highlights a focusing behavior near an early-universe critical point and shows that perturbations must be studied to confront these couplings with observations. These results motivate observational tests and illuminate DM decay into DE as a mechanism for late-time domination.

Abstract

Dark energy and dark matter are the dominant sources in the evolution of the late universe. They are currently only indirectly detected via their gravitational effects, and there could be a coupling between them without violating observational constraints. We investigate the background dynamics when dark energy is modelled as exponential quintessence, and is coupled to dark matter via simple models of energy exchange. We introduce a new form of dark sector coupling, which leads to a more complicated dynamical phase space and has a better physical motivation than previous mathematically similar couplings.

Figures (4)

• Figure 1: The region of stability (blue, shaded) in the $(b,\beta$) parameter space, for critical point D in coupling model (I).
• Figure 2: The region of stability (blue, shaded) in the $(\lambda,\alpha$) parameter space, for critical point D in coupling model (II).
• Figure 3: Phase-space trajectories for coupling model (III), with $\lambda=1$ and $\gamma=10^{-6}$. The right hand plot is the projection. The global attractor G (see Table \ref{['crit3']}) is apparent.
• Figure 4: Phase-space trajectories for coupling model (III), with $\lambda=4$ and $\gamma=10^{-6}$. This plot shows the attractor E.