Posing constraints on the free parameters of a new model of dark energy EoS: responses through cosmological behaviours

Since the late 1990's observations of type Ia Supernova, our universe is predicted to experience a late time cosmic acceleration. Theoretical support to this observation were intended to be built via proposition of a hypothetical fluid which staying inside the universe exerts negative pressure. Cosmologists have prescribed many candidates for this exotic fluid so far. In this alley, a popular method is to choose time dependent equation of state parameter omega=p/rho and to parametrize it as a function of redshift. Again some common families of such parametrizations are constructed among which different members justify different properties of observed universe. Mainly, these were model dependent studies which comprise free parameters to be constrained by different observations. In this present article, a new expression for redshift parametrization is considered and we have constrain its free parameters for two Hubble parameter vs redshift data sets. These data sets are obtained depending on two basic methodologies known as different ages method and baryonic acoustic oscillation method. Different confidence contours for our model are located under the constraints of said data sets. Besides, different thermodynamic parameters related to the evolution of our universe are analysed. It is notified that our model indicates towards a delayed dark matter model which mimics EoS = -1(Lambda) phenomena at the present epoch. Deceleration parameters behaviour's are studied. It is noticed that a possibility of future deceleration may occur for this new model. Outcomes for both the data sets are compared with each other.