Cosmological implications of quantum mechanics parametrization of dark energy

We consider the cosmology with the running dark energy. The parametrization of dark energy is derived from the quantum process of transition from the false vacuum state to the true vacuum state. This model is the generalized interacting CDM model. We consider the energy density of dark energy parametrization, which is given by the Breit-Wigner energy distribution function. The idea of the process of the quantum mechanical decay of unstable states was formulated by Krauss and Dent. We used this idea in our considerations. In this model is an energy transfer in the dark sector. In this evolutional scenario the universe starts from the false vacuum state and goes to the true vacuum state of the present day universe. The intermediate regime during the passage from false to true vacuum states takes place. In this way the cosmological constant problem can be tried to solve. We estimate the cosmological parameters for this model. This model is in a good agreement with the astronomical data and is practically indistinguishable from CDM model.