Recently, the vacuum energy of the QCD ghost field in a time-dependent background was proposed as a kind of dark energy candidate called the ghost dark energy model (GDE) to explain the acceleration of the Universe. In this model, the energy density of the dark energy is proportional to the Hubble parameter $H$, which is also regarded as the Hawking temperature on the Hubble horizon of the Friedmann-Robertson-Walker Universe. In this paper, the statefinder and $Om$ diagnostics are applied to the GDE models, and the differences among them are significant during the time of transition. And at that time, the viscosity plays an important role. Furthermore, we find that once the viscosity is taken into account, the age problem of Universe could be alleviated. We also perform a constraint on the GDE models with and without bulk viscosity by using the Markov Chain Monte Carlo method and the combined latest observational data from the type Ia supernova compilations including Union2.1(580) and Union2(557), cosmic microwave background, baryon acoustic oscillation, and the observational Hubble parameter data.

• Received 17 January 2012

DOI:https://doi.org/10.1103/PhysRevD.87.023006