Observational constraints on FRW cosmologies with dark energy-dark matter interaction

In this paper, within the scope of FRW cosmology for $k=0, \pm 1$ , we investigate the dynamics of the universe in cosmological model where a scalar field nonminimally is coupled to matter field. By best-fitting the model parameters with the observational data, for the direct interaction between the dark sectors in the model, we obtain new constraints on cosmological parameters. The result with the best fitted model parameters supports the current universe acceleration in all models and shows that only in flat universe case the phantom crossing occurs twice in the past and once in the future. The best fitted reconstructed potential function and other physical functions are also obtained.