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We consider a cosmology with decaying metastable dark energy and assume thata decay process of this metastable dark energy is a quantum decay process. Suchan assumption implies among others that the evolution of the Universe isirreversible and violates the time reversal symmetry. We show that if toreplace the cosmological time $t$ appearing in the equation describing theevolution of the Universe by the Hubble cosmological scale time, then we obtaintime dependent $\Lambda (t)$ in the form of the series of even powers of theHubble parameter $H$: $\Lambda (t) = \Lambda (H)$. Out special attention isfocused on radioactive like exponential form of the decay process of the darkenergy and on the consequences of this type decay.

From quantum unstable systems to the decaying dark energy: Cosmological implications