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This study forges new tools to discriminate between dynamical and static dark energy. It provides accurate evolutionary templates of dynamical cosmological parameters and fundamental constants as analytic functions of the scale factor. They are designed to replace the commonly used parameterizations in likelihood calculations with evolutionary templates based on the physics of specific dynamical cosmologies and dark energy potentials. Thus they are termed Cosmology and Potential Specific, CPS, templates. A suite of CPS templates are calculated for a flat quintessence cosmology with a dark energy potential of the same mathematical form as the Higgs potential. This Higgs inspired, HI, polynomial potential produces a rich set of evolutions unlike most monomial potentials. The study produces CPS templates that are analytic functions of the scale factor. It uses a recently developed beta function formalism that provides a differential function for the scalar in terms of the scale factor. This establishes a methodology for easily producing CPS templates for other dark energy potentials and cosmologies to determine the likelihoods of dynamical cosmologies relative to Lambda CDM. The study also examines the evolution of fundamental constants such as the proton to electron mass ratio and the fine structure constant involving an intersection between particle physics and cosmology. Appendix A displays an abridged suite of CPS templates for flat quintessence and the HI dark energy potential.