A New Parametrization Framework for Dark Energy and Total Cosmic Fluid

A novel parametrization of the Equation of State (EoS) for a dynamic dark energy is introduced and its consequences in cosmology including the late time transition from a decelerating expansion to an accelerating expansion of the universe are investigated. We introduce a simple parametrization of EoS for the dynamic dark energy using a smooth sigmoid function that contains a transition redshift ( ) at which a switch over in the dynamics of the universe observed to be occurred. The present parametrization involves three model parameters ,  and  constrained by the observational values of cosmological parameters from recent cosmological data. This EoS model introduces a continuous and smooth transition between matter-dominated and dark energy-dominated epochs as well. Such a parametrization enables dark energy to influence the late time cosmic dynamics of the universe without disturbing the early expansion dynamics involving cosmic microwave background radiation of the universe. We formulate the corresponding Friedmann theoretical framework through cosmological parameters like Hubble parameter, density parameter and deceleration parameter. It is then generalised to the total effective EoS parameter by the same function. By performing an analytical study of the cosmological parameters, the proposed model is compared with the standard cosmological model. The constraints derived for the sigmoid-based phenomenological dark energy parametrization describes its wide applicability to dynamic dark energy models that account for late-time cosmic acceleration and the overall evolution of the universe.