Effects of particle creation rate in two-fluid interacting cosmologies

In this work, a two-fluid interacting model in a flat FLRW universe has been studied considering particle creation mechanism with a particular form of particle creation rate $\Gamma=\Gamma_0 H+\frac{\Gamma_1}{H}$ from different aspects. Statistical analysis with a combined data set of SNe Ia (Supernovae Type Ia) and Hubble data is performed to achieve the best-fit values of the model parameters, and the model is compatible with current observational data. We also perform a dynamical analysis of this model to get an overall qualitative description of the cosmological evolution by converting the governing equations into a system of ordinary differential equations considering a proper transformation of variables. We find some non-isolated sets of critical points, among which some usually are normally hyperbolic sets of points that describe the present acceleration of the universe dominated by dark energy mimicking cosmological constant or phantom fluid. Scaling solutions are also obtained from this analysis, and they can alleviate the coincidence problem successfully. Statefinder diagnosis is also carried out for this model to compare it with the $\Lambda$CDM, and any other dark energy models by finding various statefinder parameters. Finally, the thermodynamic analysis shows that the generalized second law of thermodynamics is valid in an irreversible thermodynamic context.