Differentiating dark interactions with perturbation

A cosmological model with an energy transfer between dark matter (DM) and (DE) can give rise to comparable densities at the present epoch. The work deals perturbation analysis, parameter estimation Bayesian evidence calculation of interacting models dynamical coupling that determines strength interaction. We have considered two cases, where interaction is a more recent phenomenon in distant past. Moreover, we quintessence DE equation state Chevallier-Polarski-Linder (CPL) parametrisation flow from DM DE. Using current observational datasets like cosmic microwave background (CMB), baryon acoustic oscillation (BAO), Type Ia Supernovae (SNe Ia) redshift-space distortions (RSD), estimated mean values parameters. analysis calculation, shown as brief early preferred over