Cosmological coincidence problem in interacting dark energy models

Abstract

The interacting dark energy model with interaction term $Q={\ensuremath{\lambda}}_{m}H{\ensuremath{\rho}}_{m}+{\ensuremath{\lambda}}_{d}H{\ensuremath{\rho}}_{d}$ is considered. By studying the model near the transition time, in which the system crosses the $\ensuremath{\omega}=\ensuremath{-}1$ phantom divide line, the conditions needed to overcome the coincidence problem is investigated. The phantom model, as a candidate for dark energy, is considered, and for two specific examples, the quadratic and exponential phantom potentials, it is shown that it is possible the system crosses the $\ensuremath{\omega}=\ensuremath{-}1$ line, meanwhile the coincidence problem is alleviated, the two facts that have root in observations.