  A solution to Einstein's field equations via the Friedman equations is shown
to produce a cosmological model that is in exact agreement with the
measurements made by the dark energy astronomers. All the essential physical
parameters are obtained as epoch dependent functions all in closed form. The
equations of state are obtained for total density, non-dark energy density and
dark energy density. An interpretation of the structure involving a dark energy
mass distribution that is twice the usual value is shown to clarify greatly the
physical significance of the mathematics. It is asserted that the astronomer's
measurements together with the mathematical model proves that the universe is
permeated uniformly with a positive mass density that caries a negative
gravitational constant, -G, characteristic. This mass component is identified
with the dark energy content of the universe that has been postulated to
explain the observed acceleration. Another result implied by the model is that
there is twice the amount of dark energy that is usually considered to be
present. This last point is analysed in more detail in appendix 1 using
Einstein's field equations. Five additional appendices, 2, 3, 4, 5 and 6 in
which isothermal gravitational dark matter equilibrium and the galactic
rotations curve flatness problem are examined in detail. Appendix 5 is
concerned with mass clumping and expressing gravitational isothermal
equilibrium constraints using a cosmological Schr\"odinger equation to
demonstrate the existence of a new quantum force involved with galactic
stability. Appendix 6 is concerned with gravitational quantization. Each
appendix has its own abstract.
