Using a phenomenological model to test the coincidence problem of dark energy

TL;DR

This paper tests the cosmic coincidence problem using a phenomenological model relating dark energy and dark matter densities, constrained by observational data, and finds that the coincidence problem remains significant within this framework.

Contribution

It introduces a phenomenological model with a scaling parameter to analyze the coincidence problem and constrains it with current observational data, reaffirming the problem's severity.

Findings

The model fits observational data well, consistent with mbda CDM.

The coincidence problem remains severe in this framework.

Interaction between dark energy and dark matter is necessary if transition redshift exceeds 0.73.

Abstract

By assuming a phenomenological form for the ratio of the DE and DM densities $\rho_X\propto \rho_{m} a^{\xi}$ (Dalal et al.2001), we discuss the cosmic coincidence problem in light of current observational data. $\xi$ is a key parameter to denote the severity of the coincidence problem. In this scenario, $\xi=3$ and $\xi=0$ correspond to $\Lambda$CDM and the self-similar solution without coincidence problem, respectively. Hence, any solution with a scaling parameter $0<\xi<3$ makes the coincidence problem less severe. In addition, the standard cosmology without interaction between DE and DM is characterized by $\xi+3\omega_X=0$, whereas the inequality $\xi+3\omega_X\neq 0$ represents non-standard cosmology. We place observational constraints on the parameters $(\Omega_{X,0},\omega_{X},\xi)$ of this model, by using the Constitution Set, the CMB shift parameter from the 5-year WMAP and the SDSS baryon acoustic peak. Combining the three samples, we get $\Omega_{X,0}=0.72\pm0.02$, $\omega_{X}=-0.98\pm0.07$ and $\xi=3.06\pm0.35$ at 68.3% confidence level. The result shows that the $\Lambda$CDM model still remains a good fit to the recent observational data, as well as, the coincidence problem indeed exists and is quite severe, in the framework of this simple phenomenological model. We further constrain the model with the transition redshift (deceleration / acceleration). It shows that if the transition from deceleration to acceleration happens at the redshit $z > 0.73$, within the framework of this model, we can conclude that the interaction between DE and DM is necessary.