Holography, UV/IR Relation, Causal Entropy Bound, and Dark Energy

The constraint on the total energy in a given spatial region is given from holography by the mass of a black hole that just fits in that region, which leads to an UV/IR relation: the maximal energy density in that region is proportional to M_p²/L², 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_CC. For gravitationalperturbations, R^-2_CC= Max (\dot{H}+2H² -\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 thecases 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^-2_CC= \dot{H} +2H², could be consistent with the current cosmological observations when the vacuum density appears asan independently conserved energy component. In this case, the model is called holographic Ricci scalar dark energy model in the literature.