The Lagrangian
The Lagrangian L is
The principle of least action is
where g is the determinant of the symmetric metric tensor.
For arbitary variation of and its complex conjugate leads to the equations
which leaves
Now
The integral becomes
which simplifies to
which gives the field equations
Which is equivalent to
This gives  and therefore
The equation for the Boson can be written as
Which is the result of applying a  gauge transformation  of
Thus the gauge field is related to the curvature scalar G by the relation
Where g is a coupling constant.

 
 

Gauge Transformation Of The Curvature Scalar G
The Lagrangian must be invariant under the local gauge transformation
The curvature tensor is
contracting and ignoring the asymmetric connection terms yields G
The symmetric connection transforms as
The curvature scalar transforms as
Substituting the transformed connection results in
which simplifies to
where
The Weak field approximation for the metric tensor is
in this approximation reduces to
The Schwarzchild solution gives
For
Where  will be shown to be the source of the Dark Energy.