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

We consider a cosmology with decaying metastable dark energy and assume that a decay process of this metastable dark energy is a quantum decay process. Such an assumption implies among others that the evolution of the Universe is irreversible and violates the time reversal symmetry. We show that if to replace the cosmological time $t$ appearing in the equation describing the evolution of the Universe by the Hubble cosmological scale time, then we obtain time dependent $\mathrm{\Lambda }(t)$ in the form of the series of even powers of the Hubble parameter $H$: $\mathrm{\Lambda }(t)=\mathrm{\Lambda }(H)$. Out special attention is focused on radioactive like exponential form of the decay process of the dark energy and on the consequences of this type decay.