Equation of state and background geometry for the accelerating universe

Abstract

By using the observational data, we show that the background geometry for both the early inflation and present accelerating universe can be quasi-de Sitter form containing cosmic fluid with equation of state [Formula: see text], where [Formula: see text]. For the dynamical expanding background of the universe, we obtain the scale factor as a function of conformal time [Formula: see text] and Hankel function index [Formula: see text]. Since the background geometry of the universe is related to the index [Formula: see text], a direct relation between the geometry [Formula: see text] and the equation of state parameter [Formula: see text] will be obtained. By using this fact and the constraints on the scalar spectral index and equation of state from Planck 2015, our calculations show that the cosmic fluid of the present accelerating universe is contained with both phantom [Formula: see text] and non-phantom [Formula: see text] phases, but the cosmic gas during inflation is contained with just non-phantom [Formula: see text] phase. Also, the background geometry for both early inflation and present accelerating universe is inferred to be quasi-de Sitter form with [Formula: see text].