  In general, a global and unique vacuum state cannot be constructed for a
curved space. As a remedy, we introduce a curved space background geometry with
a Minkowski metric tensor and locally non-zero curvature and torsion. Based on
this geometry, we propose a `third'/vacuum quantization model as a consequence
of Unruh effect. Accordingly, we introduce a `third' quantization scalar field
as a general coordinate transformation of spacetime for the second quantization
fields. Then we show that in the classical limit, the `third' quantization
fields appear as Riemannian manifolds with an emergent metric on which the
second quantization fields are located. This way, the standard model of field
theory turns out as an effective theory. Moreover, using the proposed `third'
quantization fields, we build a $U(1)\times SU(4)$ Yang-Mills gauge theory for
gravity. According to this gravitational model, we indicate that an analytical
solution of the presented gravitational model, for the `third' quantum field
particle trajectory (such as a star), corresponds to the trajectory of a test
particle in the Mannheim-Kazanas space. Furthermore, by using non-perturbative
methods and lattice gauge theory results, we render a solution for the
potential of the constructed model that can explain the galaxy rotation curves
and gravitational lensing without any need to dark matter. We also address the
cosmic microwave background phenomenon and the expansion of the universe.
