Toward a solution of the coincidence problem

The coincidence problem of late cosmic acceleration constitutes a serious riddle with regard to our understanding of the evolution of the Universe. Here we argue that this problem may someday be solved—or better understood—by expressing the Hubble expansion rate as a function of the ratio of densities (dark matter/dark energy) and observationally determining the said rate in terms of the redshift.

Figure 1

Evolution of the ratio $r={\rho }_m/{\rho }_{\varphi }$ with redshift for different values of the parameter $\alpha$. In drawing the curves we have fixed $r_0=3/7$ and $w=-0.9$.

Figure 2

Evolution $H$ vs the ratio $r={\rho }_m/{\rho }_{\varphi }$ as given by Eq. (8) with $\alpha ={10}^{-4}$ for $w=-0.9$ (quintessence, top line) and $w=-1.1$ (phantom, bottom line). Also shown is the prediction of the $\Lambda \mathrm{CDM}$ model (middle line). In drawing all the curves we have fixed $r_0=3/7$.

Figure 3

Evolution $H$ vs $z$ with $\alpha ={10}^{-4}$ for $w=-0.9$ (quintessence) and $w=-1.1$ (phantom). Also shown is the prediction of the $\Lambda \mathrm{CDM}$ model (solid line). In all the cases we have fixed $r_0=3/7$ and $H_0=71\mathrm{km}/\mathrm{s}/\mathrm{Mpc}$. The data points with their $1\sigma$ error bars are borrowed from Simon, Verde, and Jiménez, Ref. 14 (full circles), and Table 2 of Ref. 15 (full diamonds).

Figure 4

Same as Fig. 3. The upper panel shows the combined sample of 132 SN Ia of Ref. 19 and 30 radio galaxies of Ref. 20. The bottom panel shows the 30 radio galaxies only. The data points with their $1\sigma$ error intervals and the best-fit curve (big solid line) in both panels are borrowed from Daly et al., Ref. 15.

Figure 5

Evolution of the ratio $r={\rho }_m/{\rho }_{\varphi }$ with redshift for different values of the parameter $\beta$. In drawing both curves we have fixed $r_0=3/7$ and $w=-0.9$. As it is apparent, $\dot{r}/r\simeq 0$ at late times.