Testing the coincidence problem with strong gravitational lens, Type Ia supernovae and Hubble parameter observational data

TL;DR

This study combines gravitational lensing, supernovae, and Hubble data to test the coincidence problem and constrain a phenomenological dark energy model, finding that the standard Lambda-CDM model remains the best fit.

Contribution

It introduces a combined observational approach to constrain a specific dark energy-dark matter interaction model and assesses the coincidence problem's status.

Findings

Lambda-CDM remains the best fit to data.

The coincidence problem is not alleviated.

Transition redshift is approximately 0.645.

Abstract

In this paper, we use three different kinds of observational data, including 130 strong gravitational lensing (SGL) systems, type Ia supernovae (SNeIa: Pantheon and Union2.1) and 31 Hubble parameter data points ($H(z)$) from cosmic chronometers to constrain the phenomenological model ($\rho_x\varpropto\rho_m a^{\xi}$). By combining these three kinds of data (Union2.1+SGL+$H(z)$), we get the parameter value at the confidence interval of $2\sigma$, $\Omega_{X,0} = 0.69\pm0.34$, $\omega_x = -1.24\pm0.61$, $\xi = 3.8\pm3.9$ and $H_0 = 70.22\pm0.86$ kms$^{-1}$Mpc$^{-1}$. According to our results, we find that the $\Lambda$CDM model is still the model which is in best agreement with the observational data at present, and the coincidence problem is not alleviated. In addition, the $\Omega_X$ and $\Omega_m$ have the same order of magnitude in $0<z<1.26$. At last, we obtain the transition redshift $z_T=0.645$. If the transition occurs in $z>0.645$, it is necessary to introduce the dark energy interacting with dark matter.