Interacting dark matter and modified holographic Ricci dark energy plus a noninteracting cosmic component

We investigate a spatially flat Friedmann-Robertson-Walker universe that has an interacting dark matter, a modified holographic Ricci dark energy (MHRDE), plus a third, decoupled component that behaves as a radiation term. We consider a nonlinear interaction in the dark component densities and their derivatives up to second order. We apply the $\chi^{2}$ method to the observational Hubble data for constraining the cosmological parameters and analyze the amount of dark energy in the radiation era for both MHRDE and holographic Ricci dark energy models. The former is consistent with the bound $\Omega_{x}(z\simeq 1100)<0.1$ reported for the behavior of dark energy at early times while the latter does not fulfill it.