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