Emulating dark energy models with known equation of state via the created cold dark matter scenario

In this work we establish only at background dynamics level, the equivalence between the Created Cold Dark Matter (CCDM) model and diverse dark energy (DE) models. We find that for a barotropic or linear equation of state (EoS) for the DE, $p=w\rho$, and standard matter sector the corresponding CCDM model is described by the same functional structure of the ratio of particle production, $\mathrm{\Gamma }$. For a different EoS the functional form of the $\mathrm{\Gamma }$ term is not longer maintained, however, in the case of a polytropic EoS given by the Chaplygin gas the resulting $\mathrm{\Gamma }$ term can be written as the one obtained in the barotropic case under certain considerations.