Abstract
Based on quantum mechanics and general relativity, Karolyhazy proposed a generalization to the well-known Heisenberg uncertainty relation in which the energy density of quantum fluctuations of space-time plays a crucial role. Later on, various holographic DE models were suggested, in which the Hubble scale (size) and the age of the universe were assumed as measures for the largest infrared cutoff satisfying the holographic principle and energy bounds assuring applicability of quantum field theory. We review various models based on the holographic principle and the Karolyhazy relation and compare these to the space-time foam and superconducting DE models. We analyze their (in)stability against cosmological perturbation.
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