A quintessence dynamical dark energy model from ratio gravity

Based on the work of ratio gravity developed in 2018, which postulates deformation cross to associate with physical model gravity, we develop a mechanism generate dynamical dark energy - quintessence field coupled gravity. Such causes behaving differently early and late time universe. In radiation-dominated-era matter-dominated-era, related analytical solutions have an interesting property starting as constant field, then oscillating universe expands. By Markov Chain Monte Carlo search parameter space local measurement (Type Ia supernovae) Bayesian framework, probed range {H_0} (within 1{\sigma}) overlaps value inferred from Planck CMB dataset by {\Lambda}CDM model.