Long time deviations from the exponential decay law: possible effects in
  particle physics and cosmology
  An effect generated by the nonexponential behavior of the survival amplitude
of an unstable state in the long time region is considered. We find that the
instantaneous energy of the unstable state for a large class of models of
unstable states tends to the minimal energy of the system ${\cal E}_{min}$ as
$t\rightarrow\infty$ which is much smaller than the energy of this state for
$t$ of the order of the lifetime of the considered state. Analyzing the
transition time region between exponential and non-exponential form of the
survival amplitude we find that the instantaneous energy of the considered
unstable state can take large values, much larger than the energy of this state
for $t$ from the exponential time region. Taking into account results obtained
for a model considered, it is hypothesized that this purely quantum mechanical
effect may be responsible for the properties of broad resonances such as
$\sigma$ meson as well as having astrophysical and cosmological consequences.
