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 $\Lambda (t)$ in the form of the series of even powers of the
Hubble parameter $H$: $\Lambda (t) = \Lambda (H)$. 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.
