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In the holographic Ricci dark energy (RDE) model, the parameter $\alpha$plays an important role in determining the evolutionary behavior of the darkenergy. When $\alpha<1/2$, the RDE will exhibit a quintom feature, i.e., theequation of state of dark energy will evolve across the cosmological constantboundary $w=-1$. Observations show that the parameter $\alpha$ is indeedsmaller than 1/2, so the late-time evolution of RDE will be really like aphantom energy. Therefore, it seems that the big rip is inevitable in thismodel. On the other hand, the big rip is actually inconsistent with thetheoretical framework of the holographic model of dark energy. To avoid the bigrip, we appeal to the extra dimension physics. In this Letter, we investigatethe cosmological evolution of the RDE in the braneworld cosmology. It is ofinterest to find that for the far future evolution of RDE in a Randall-Sundrumbraneworld, there is an attractor solution where the steady state (de Sitter)finale occurs, in stead of the big rip.

Holographic Ricci dark energy in Randall-Sundrum braneworld: Avoidance of big rip and steady state future