  Dark energy is a fundamental constituent of our universe, its status in the
cosmological field equation should be equivalent to that of gravity. Here we
construct a dark energy and matter gravity coupling (DEMC) model of cosmology
in a way that dark energy and gravity are introduced into the cosmological
field equation in parallel with each other from the beginning. The DEMC
universe possesses a composite symmetry from global Galileo invariance and
local Lorentz invariance. The observed evolution of the universe expansion rate
at redshift z>1 is in tension with the standard LCDM model, but can be well
predicted by the DEMC model from measurements of only nearby epochs. The so far
most precise measured expansion rate at high z is quite a bit slower than the
expectations from LCDM, but remarkably consistent with that from DEMC. It is
hoped that the DEMC scenario can also help to solve other existing challenges
to cosmology: large scale anomalies in CMB maps and large structures up to
about 10^3 Mpc of a quasar group. The DEMC universe is a well defined
mechanical system. From measurements we can quantitatively evaluate its total
rest energy, present absolute radius and expanding speed.
