2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/192840We investigate a model of brane cosmology to find a unified description of the radiation-matter-dark energy universe. It is of the interacting holographic dark energy with a bulk-holographic matter $χ$. This is a five-dimensional cold dark matter, which plays a role of radiation on the brane. Using the effective equations of state $ω^{\rm eff}_{\rm Λ}$ instead of the native equations of state $ω_{\rm Λ}$, we show that this model cannot accommodate any transition from the dark energy with $ω^{\rm eff}_{\rm Λ}\ge-1$ to the phantom regime $ω^{\rm eff}_{\rm Λ}<-1$. Furthermore, the case of interaction between cold dark matter and five dimensional cold dark matter is considered for completeness. Here we find that the redshift of matter-radiation equality $z_{\rm eq}$ is the same order as $z^{\rm ob}_{\rm eq}=2.4\times10^{4} Ω_{\rm m}h^2$. Finally, we obtain a general decay rate $Γ$ which is suitable for describing all interactions including the interaction between holographic dark energy and cold dark matter.17 pages, 4 figuresGeneral Relativity and Quantum CosmologyAstrophysicsHigh Energy Physics - Theorytext