Interaction of polytropic dark energy in cosmological model: Constraints from observational data

We investigate an interacting polytropic dark energy model characterized by the equation of state (EoS), [Formula: see text], where the interaction between dark energy and pressureless matter is modeled via a linear coupling term [Formula: see text]. The background dynamics are formulated by deriving the Hubble parameter in the interacting scenario, and the model parameters are constrained through a Markov Chain Monte Carlo (MCMC) analysis using three joint observational datasets: Hubble+BAO, Hubble+Pantheon[Formula: see text], and Hubble+BAO+Pantheon[Formula: see text]. The resulting best-fit values of [Formula: see text] are [Formula: see text], [Formula: see text], and [Formula: see text] respectively, for the respective data combinations. Our results indicate a positive energy density and negative pressure over the full redshift range, with the evolution of the equation of state parameter and state finder parameters placing the model firmly within the Quintessence regime. The study of the deceleration parameter also reveals a shift from a decelerating to an accelerating cosmic expansion. The study of EoS for the polytropic DE, suggests that our Universe is characterized by a Phantom-like behavior. The estimated present age of the Universe is 14[Formula: see text]Gyr, consistent with recent observational data. Furthermore, the sign of Q implies a current energy transfer from dark energy to matter. These findings support the interacting PDE framework as a viable candidate for explaining late-time cosmic acceleration and related large-scale dynamics.