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This study forges new tools to discriminate between dynamical and static darkenergy. It provides accurate evolutionary templates of dynamical cosmologicalparameters and fundamental constants as analytic functions of the scale factor.They are designed to replace the commonly used parameterizations in likelihoodcalculations with evolutionary templates based on the physics of specificdynamical cosmologies and dark energy potentials. Thus they are termedCosmology and Potential Specific, CPS, templates. A suite of CPS templates arecalculated for a flat quintessence cosmology with a dark energy potential ofthe same mathematical form as the Higgs potential. This Higgs inspired, HI,polynomial potential produces a rich set of evolutions unlike most monomialpotentials. The study produces CPS templates that are analytic functions of thescale factor. It uses a recently developed beta function formalism thatprovides a differential function for the scalar in terms of the scale factor.This establishes a methodology for easily producing CPS templates for otherdark energy potentials and cosmologies to determine the likelihoods ofdynamical cosmologies relative to Lambda CDM. The study also examines theevolution of fundamental constants such as the proton to electron mass ratioand the fine structure constant involving an intersection between particlephysics and cosmology. Appendix A displays an abridged suite of CPS templatesfor flat quintessence and the HI dark energy potential.

Dynamical templates for comparison to Lambda CDN: Static or dynamical dark energy?