Stationary dark energy: the present universe as a global attractor

Abstract

We propose a cosmological model that makes a significant step toward solving the coincidence problem of the near similarity at the present of the dark energy and dark matter components. Our cosmology has the following properties: a) among flat and homogeneous spaces, the present universe is a global attractor: all the possible initial conditions lead to the observed proportion of dark energy and dark matter; once reached, it remains fixed forever; b) the expansion is accelerated at the present, as requested by the supernovae observations; c) the model is consistent with the large-scale structure and microwave background data; d) the dark energy and the dark matter densities always scale similarly after equivalence and are close to within two orders of magnitude. The model makes use of a non-linear coupling of the dark energy to the dark matter that switches on after structure formation.

Figures (3)

• Figure 1: Top panel. Trends of $\Omega _{\gamma }$ (dashed line), $\Omega _{m}$ (dotted), and $\Omega _{\phi }$ (continuous) versus $\log a$. The three regimes mentioned in the text are evident: first, radiation dominates, then matter dominates (plateau I), and then finally the system falls on the final accelerated attractor (plateau II) with 30% of dark matter and 70% of dark energy. The constants have been chosen here as $\mu =30$ , $\beta _{1}=0$ and $\beta _{2}=70$. Bottom panel. The effective parameter of state $w_{eff}$ during the three regimes: first equals $4/3$, then goes down to $1,$ and finally becomes accelerated, $w_{eff}=0.3$.
• Figure 2: The plot shows the behavior of $\rho _{\phi }/\rho_m$ in our model (continuous lines) for different initial conditions, and in an inverse power-law model without coupling (dotted line). The vertical line is the present time. In the coupled model the ratio is close to unity ever after equivalence.
• Figure 3: Parameter space of the model. To the right of the short-dashed line the expansion is accelerated; above the long-dashed line the nucleosynthesis constraint is passed. The parameters within the gray region on the left produce enough structure formation. Those inside the gray region on the right yield an accelerated expansion with $\Omega _{\phi }$ between 0.6 and 0.8 (the continuous line is $\Omega _{\phi }=0.7$). Any coupling function that switches from the first region to the second after structure formation gives an acceptable model. The two asterisks mark the effective parameters we employed in the numerical calculations.