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

We investigate an interacting polytropic dark energy model characterised by the equation of state (EoS), [Formula: see text], where the interaction between dark energy and pressureless matter is modelled 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 data sets: 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 characterised by a Phantom-like behavior. The estimated present age of the Universe is [Formula: see text], consistent with recent observational data. Furthermore, the sign of [Formula: see text] 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.