  The constraint on the total energy in a given spatial region is given from
holography by the mass of a black hole which just fits in that region, which
leads to an UV/IR relation: the maximal energy density in that region is
proportional to $M_p^2/L^2$, where $M_p$ is the Planck mass and $L$ is the
spatial scale of that region under consideration. Assuming the maximal black
hole in the universe is formed through gravitational collapse of perturbations
in the universe, then the "Jeans" scale of the perturbations gives a causal
connection scale $R_{\rm CC}$. For gravitational perturbations, $R^{-2}_{\rm
CC}={\rm Max}(\dot H+2H^2, -\dot H)$ for a flat universe. We study the
cosmological dynamics of the corresponding vacuum energy density by choosing
the causal connection scale as the IR cutoff in the UV/IR relation, in the
cases of the vacuum energy density as an independently conserved energy
component and an effective dynamical cosmological constant, respectively. It
turns out that only the case with the choice $R_{\rm CC}^{-2}= \dot H +2H^2$,
could be consistent with the current cosmological observations when the vacuum
density appears as an independently conserved energy component. In this case,
the model is called holographic Ricci scalar dark energy model in the
literature.
