Cosmological Dynamics of Matter Creation with Modified Chaplygin Gas and Bulk Viscosity

Abstract: This work presents a comprehensive investigation of a novel cosmological model that unifies the Modified Chaplygin Gas (MCG) equation of state with gravitationally induced matter creation and bulk viscous dissipation in a spatially flat Friedmann-Lemaitre-Robertson-Walker spacetime. The MCG fluid is characterized by an exotic equation of state $p = A\rho - C/\rho^\alpha$, while the matter creation rate is taken as $\Gamma = 3\beta H$ and the bulk viscous pressure as $\pi = -3H\xi_0 \rho_m^{1/2}$. We derive the modified Friedmann equations and obtain an analytical expression for the Hubble parameter $H(z)$, which is then used to reconstruct the evolutionary trajectories of key cosmological parameters: the deceleration parameter $q(z)$, jerk parameter $j(z)$, and snap parameter $s(z)$. The model parameters are constrained using two observational datasets: DS1 (Pantheon+ + Cosmic Chronometers + DESI BAO + $\sigma_8$) and DS2 (DS1 + R22), employing a Markov Chain Monte Carlo (MCMC) analysis. The results indicate that the proposed hybrid model successfully generates a transition from decelerated to accelerated expansion, consistent with current observations. Notably, the inclusion of R22 data leads to a higher best-fit value of $H_0$, helping to alleviate the $H_0$ tension. Furthermore, we perform a rigorous thermodynamic analysis of the model by testing the Generalized Second Law (GSL) of thermodynamics. We compute the total entropy rate of change $\dot{S}{\text{total}} = \dot{S}{\text{fluid}} + \dot{S}{\text{horizon}}$, finding it positive throughout cosmic history for both datasets, confirming the model's thermodynamic viability. The second derivative $\ddot{S}{\text{total}}$ exhibits a clear transition from positive to negative values around $z \sim 1$, indicating a shift from accelerating to decelerating entropy production a signature of late-time thermodynamic stabilization.