  Decaying vacuum models are a class of models that incorporate the vacuum
energy density as a time-evolving entity that has the potential to explain the
entire evolutionary history of the universe in a single framework. A general
solution to the Friedmann equation can be obtained by considering vacuum energy
density as a function of the Hubble parameter. We have obtained the asymptotic
solution by choosing the appropriate equation of state for matter and
radiation. Finite boundaries in the early and late de Sitter epoch could be
defined by considering the evolution of primordial perturbation wavelength. An
epoch invariant number $N_c$ determines the number of perturbation modes that
cross the Hubble radii during each epoch has been obtained.
