2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/57784The 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.27 pages,2 figuesMathematical Physics85A40;81V17text