Early homogeneous universe with variable cosmological constant: Kinematics tests

A spatially homogeneous cosmological model with flat geometry filled with perfect fluid is studied in the presence of a variable cosmological "constant." Einstein's field equations are solved by using the "gamma-law" equation of state p = (gamma - 1)rho, where the adiabatic parameter -, varies with cosmic time. The functional form of gamma, which is assumed to be the function of scale factor R as proposed by Carvalho, is used to describe the early evolution of universe with variable cosmological "constant." A unified description of early universe is given in which an inflationary phase is followed by radiation-dominated phase. It has been observed that the solutions are compatible with the result of recent observations. Exact expressions for the look-back time, proper distance, luminosity distance and angular diameter distance versus redshift are derived and their meaning are discussed in detail. The various physical aspects of the models are also discussed.