Variable Cosmological Constant model: the reconstruction equations and constraints from current observational data

Abstract

In this paper we first give a brief review of the variable cosmological constant model and its scalar field description. We mainly discuss two types of variable cosmological constant models: $a$ power law and $H$ power law models. A method to obtain all of the equivalent scalar field potentials and the effective equation of state of the two models is presented. In addition, the dynamics of such scalar field potentials and effective equation of state are discussed in detail. The parameters of the two models are constrained by current 307 high-quality "Union" SN Ia data set, baryon acoustic oscillation (BAO) measurement from the Sloan Digital Sky Survey (SDSS), 9 observational \textrm{H(z)} data derived from the Gemini Deep Deep Survey (GDDS) and the shift parameter of the cosmic microwave background (CMB) given by the three-year Wilkinson Microwave Anisotropy Probe (\textrm{WMAP}) observations. We also calculate and draw the picture of the Hubble parameter, the deceleration parameter and the matter density of the two models. Then, we show that the indices $m$ and $n$ in the two models have specific meaning in determining properties of the models. Moreover, The reasons that indices $m$ and $n$ may also influence the behavior of effective equation of state and scalar field potentials are presented.