Interacting dark energy and the cosmic coincidence problem

The introduction of an interaction for dark energy to the standard cosmology offers a potential solution to the cosmic coincidence problem. We examine the conditions on the dark energy density that must be satisfied for this scenario to be realized. Under some general conditions we find a stable attractor for the evolution of the Universe in the future. Holographic conjectures for the dark energy offer some specific examples of models with the desired properties.

Figure 1

Evolution of ${\Omega }_{\Lambda }$ (solid line) and the effective equations of state, $w_{\Lambda }^{\mathrm{eff}}$ (dashed line, bottom) and $w_m^{\mathrm{eff}}$ (dashed line, top). The horizontal axis is $x=\ln (a/a_0)$ for an arbitrary $a_0$. The future event horizon (FH) is assumed to be the length scale for determining $w_{\Lambda }^{\mathrm{eff}}$, while the interaction is given by $\Gamma /3H=b^2/\Omega$ with $b^2=0.2$.

Figure 2

Dependence of $w_{\Lambda }^{\mathrm{eff}}$ (dashed line) for the case of particle horizon (PH, top) and future event horizon (FH, bottom) and $w_m^{\mathrm{eff}}$ (solid line) for $g({\Omega }_{\Lambda })=1/{\Omega }_{\Lambda }^n$ for $n=\frac{1}{2}$, 1, $\frac{3}{2}$, 2 from top to bottom. The fixed points for the differential equation occur when $w_{\Lambda }^{\mathrm{eff}}=w_m^{\mathrm{eff}}$, and the attractive ones for large $x$ are indicated with filled squares. For the initial condition ${\Omega }_{\Lambda }=0$, the choice of FH and $n\le 1$ gives an evolution that could be consistent with observations. The parameters were assigned as $c=1$ and $b^2=0.2$.

Figure 3

Evolution of ${\Omega }_{\Lambda }$ (solid line) and the effective equations of state, $w_{\Lambda }^{\mathrm{eff}}$ (dashed line, bottom) and $w_m^{\mathrm{eff}}$ (dashed line, top) for an interaction given by $n=1/2$. The horizontal axis is $x=\ln (a/a_0)$ for an arbitrary $a_0$. The parameters used are the same as given in Fig. 2.