A Dark Energy Model Characterized by the Age of the Universe

Quantum mechanics together with general relativity leads to the K'arolyh'azy relation and a corresponding energy density of quantum fluctuations of space-time. Based on the energy density we propose a dark energy model, in which the age of the universe is introduced as the length measure. This dark energy is consistent with astronomical data if the unique numerical parameter in the dark energy model is taken to be a number of order one. The dark energy behaves like a cosmological constant at early time and drives the universe to an eternally accelerated expansion with power-law form at late time. In addition, we point out a subtlety in this kind of dark energy model.