Some Classes of Interacting Two-Fluid Model of the Expanding Universe

We consider interacting dark matter-dark energy models arising out of a general interaction term $Q=f(\rho_{m},\rho_{d},\dot{\rho}_{m},\dot{\rho}_{d}).$ Here $f$ is a functional relation connecting the energy densities $\rho_{m}$ and $\rho_{d}$ and their derivatives w.r.t. time $t.$ In our model we consider two interacting barotropic fluid with constant equation of state $\omega_{m}$ and $\omega_{d}.$ By considering a dynamical interaction between them we trace out the cosmological evolution dynamics of the universe. We analytically solve the model by considering a constant ratio between the two fluids and then track the corresponding analytical results using observational data from the baryon acoustic oscillation measurements, Type Ia supernovae measurements and the local Hubble constant measurements. From this general setting we introduce three different models and nine different interaction function. Our final aim is to set up a comparative analysis of the various class of models under the different interaction function using common theoretical and numerical analysis.