Time arrow is influenced by the dark energy

The arrow of time and the accelerated expansion are two fundamental empirical facts of the Universe. We advance the viewpoint that the dark energy (positive cosmological constant) accelerating the expansion of the Universe also supports the time asymmetry. It is related to the decay of meta-stable states under generic perturbations, as we show on example of a microcanonical ensemble. These states will not be meta-stable without dark energy. The latter also ensures a hyperbolic motion leading to dynamic entropy production with the rate determined by the cosmological constant.