  The analyticity property of de Sitter's quantum Yang-Mills theory in the
framework of Kerin space quantization, including quantum metric fluctuation, is
demonstrated. This property completes our previous work regarding quantum
Yang-Mills theory in de Sitter's ambient space formalism, and we can construct
an axiomatic quantum field theory similar to Wightman's axioms. The color
confinement is proven for the general case, which was previously approved in
the early universe. It is shown by using the interaction between gluon fields
and the conformal sector of the gravitational field, which is a massless
minimally coupled scalar gauge field. The gluon mass results from the
interaction between the gluon fields and the massless minimally coupled scalar
field as a conformal sector of the gravitational field and then the
symmetry-breaking setting due to the vacuum expectation value of the scalar
field.
