False vacuum as an unstable state: possible cosmological implications

Recent LHC results concerning the mass of the Higgs boson indicate that the vacuum in our Universe may be unstable. We analyze properties of unstable vacuum states from the point of view of the quantum theory of unstable states. From the literature it is known that some of false vacuum states may survive up to times when their survival probability has a non-exponential form. At times much latter than the transition time, when contributions to the survival probability of its exponential and non-exponential parts are comparable, the survival probability as a function of time $t$ has an inverse power-like form. We show that at this time region the instantaneous energy of the false vacuum states tends to the energy of the true vacuum state as $1/t^{2}$ for $t \to \infty$. Properties of the instantaneous energy at transition times are also analyzed for a given model. It is shown that at this time region large and rapid fluctuations of the instantaneous energy take place. This suggests analogous behavior of the cosmological constant at these time regions.

K. Urbanowski · 2013