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Based on General Relativity (GR) we consider two different cosmologicalscenarios in where reconstruct the energy exchange (Q) between cold dark matter(DM) fluid and dark energy (DE) fluid, which is modelled with a DE varyingequation of state (EoS) parameter {\omega}. We here investigate the maincosmological effects on the growth rate of matter density perturbations(f{\sigma}8), on the effective Hubble friction term (Heff ), on the effectiveNewton constant (Geff ) and on the growth index of the linear matterfluctuations ({\gamma}). Our study demonstrates that in the coupled models theevolution of these quantities are modified with respect to the predictions inthe uncoupled models, and therefore could be used to distinguish among coupledDE scenarios. Finally, we also perform a combined statistical analysis usingcurrent observational data (geometric and dynamical probes) to put morestringent constraints on the parameters space of the cosmic scenarios studied.

Exploring the effects of a double reconstruction on the growth rate of cosmic structure, using current observational data