  The cosmological gauge field (CGF) is a classical solution of SU(2)-weak
gauge theory oscillating rapidly in time. It is the dark matter driving the CGF
cosmology. A general, local, mathematically natural construction of the CGF is
given here. The macroscopic properties are derived. The CGF is an irrotational
perfect fluid. It provides a synchronized global time coordinate and a global
rest frame. There is a conserved number density. The energy density and
pressure are related by the same equation of state as derived in the CGF
cosmology and used in the TOV stellar structure equations for stars made of CGF
dark matter. The present construction justifies the TOV solution. Some possible
routes towards testing the theory are suggested at the end.
