  In axion quintessence, the cosmological era with an energy contrast in dark
energy 0.1 < Omega_DE < 0.9 may represent a significant fraction of the
universe's lifetime if the minimum of the axion potential is negative (unstable
axion quintessence), thus resolving the cosmic coincidence problem, as pointed
out in Ref. [1]. Further details of the evolution of the quintessence field,
the scale factor of the universe, and the Hubble parameter are presented here,
focussing on models with Omega_DE,0 = 0.72 and recent dark energy average
equation of state parameter -1 < w_0 < -0.85. For these parameter values, the
contracting universe enters a late time era of kination, the negative Hubble
parameter acting like a negative friction term in the Klein-Gordon equation,
and the axion field makes many transits of--but never remains in--its vacuum
state. Robust, scaled cosmological equations are derived for simulating the
evolution of the scalar field, the scale factor, and the Hubble parameter
during a contracting phase of the universe. These equations allow the
simulations presented here to proceed much closer to the singularity at the end
of the collapsing universe than any previous simulations.
