  The tunneling Hamiltonian has proven to be a useful method in many body
physics to treat particle tunneling between different states represented as
wavefunctions. Here, we apply a generalization of the way we formed appropriate
wave functionals for CDW on how to present nucleation of an inflationary
universe. This allows us to make a generalization of the model used for
inflation where the infation is trapped in a false vacuum and, after tunning
makes a first order phase transition to initiate nucleation of an inflationary
universe, in which tunneling between states which are wave functionals between
states which wavefunctionals of a scalar quantum field are considered.We
explain how we can have particle-anti particle pairs as a model of how
nucleation occurs and construct a potential which may permit formation of dark
matter using Scherrers k-essence model construction.
