In the present study we have determined the nature of time dependence of various cosmological parameters with the help of four mathematical models. Our theoretical derivations are based on gravitational field equations (involving a dynamical cosmological constant) obtained for a homogeneous and isotropic space-time with zero curvature. In the models proposed here, we have assumed four ansatzes in the form of expressions involving the cosmological constant, Hubble parameter and time. Substituting these ansatzes into the field equations and solving them, we have derived expressions for the scale factor, Hubble parameter, deceleration parameter, energy density, gravitational constant, equation of state (EoS) parameter, cosmological constant and the relative rate of change of the gravitational constant. Using these expressions, the characteristics of time evolution of these cosmological parameters can be completely determined. Signature flip of the deceleration parameter, which is evident from astrophysical observations, has been obtained from all models of the present study. The gravitational constant has been found to be decreasing with time. The cosmological constant increases from negative to positive values while the EoS parameter decreases from positive to negative values with time. The rate of change for each of them decreases with time. It has been found that an accelerated expansion of the universe, preceded by a phase of deceleration, can also be caused by a time-independent cosmological constant with a negative value.
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