Observational constraints on a generalized equation of state model

We investigate the cosmological implications of a generalized total equation of state (EoS) model by constraining its parameters using observational datasets to effectively characterize the universe's expansion history and its dynamic properties. We introduce three parameters: $\alpha$, $\beta$, and $n$ to capture the EoS behavior across different evolutionary phases. Our analysis indicates that at high redshifts ($z \gg 1$), the EoS approaches a matter- or radiation-dominated regime, transitioning to a dark energy-dominated phase as $z \to -1$, where it tends towards a constant value $\alpha$. Using a Markov Chain Monte Carlo (MCMC) method, we analyze a combined dataset that includes 31 data points from $H(z)$ and 1701 data points from the Pantheon+ dataset. The results reveal a smooth transition from deceleration to acceleration in the universe's expansion, with current EoS values suggesting quintessence-like behavior. The model aligns with observations and indicates that dark energy is dynamically evolving rather than acting as a cosmological constant. Furthermore, energy conditions and stability analyses highlight the nature and future of dark energy. This parametrized EoS model thus offers a robust framework for understanding the complexities of dark energy and the evolution of the cosmos.