Some problems faced by the ΛCDM model (as the H0 tension) might call for new physics. In recent times, cosmologists have proposed a non-gravitational coupling between dark energy (DE) and cold dark matter (CDM) energy in order to address these issues. In doing so, the spatially homogeneous and isotropic Friedmann-Robertson-Walker (FRW) universe is filled with DE, CDM, baryons, and radiation. Furthermore, the continuity equation for the total cosmic fluid can be splitted into a system of four ordinary differential equations, where a coupling Q between DE and CDM is considered.

In this work, we study the background dynamics of the universe for two expressions of the coupling Q , namely (i) a linear combination of energy density DE and CDM, and (ii) a coupling proportional to energy density of CDM and the decelerating parameter q. These interacting models have been studied in the literature and compared with observational data so far. We compare both models by introducing the so-called Statefinder parameters r,s in addition to q, and discuss the deviations of the parametric curves r-q,r-s from ΛCDM.

Keywords: ΛCDM, interacting dark matter and dark energy, statefinder-diagnostic.