  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.
