We examine a spatially flat Friedmann-Robertson-Walker (FRW) universe filledwith interacting dark matter and a modified holographic Ricci dark energy(MHRDE). The interaction term is selected as a significant rational function ofthe total energy density and its first derivative homogeneous of degree. Weshow that the effective one-fluid obeys the equation of state of a relaxedChaplygin gas, then the universe turns to be dominated by pressureless darkmatter at early times and undergoes an accelerated expansion in the far futuredriven by a strong negative pressure. Performing a $\chi^{2}$-statisticalanalysis with the observational Hubble data and the Union2 compilation of SNeIa, we place some constraints on cosmological parameters analyzing thefeasibleness of the modified holographic Ricci ansatz. It turned that MHRDEgets the accelerated expansion faster than the $\Lambda$CDM model. Finally, anew model with a component that does not exchange energy with the interactingdark sector is presented for studying bounds on the dark energy at early times.
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