Equation of state and background geometry for the accelerating universe

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 omega approximate to -1 +/-epsilon, where epsilon << 1. For the dynamical expanding background of the universe, we obtain the scale factor as a function of conformal time tau and Hankel function index nu. Since the background geometry of the universe is related to the index nu, a direct relation between the geometry v and the equation of state parameter w 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 omega < -1 and non-phantom omega >= -1 phases, but the cosmic gas during inflation is contained with just non-phantom omega greater than or similar to -1 phase. Also, the background geometry for both early inflation and present accelerating universe is inferred to be quasi-de Sitter form with nu approximate to 1.50 +/- epsilon.