Kibble's ground-breaking 1961 paper on gravity as a local gauge theory

Sean Carroll's text book lightly touches on this at the end. Sunny
Auyang makes a short cryptic remark in her book on the philosophy of
quantum field theory that is intriguing but too incomplete.

My original unique approach to gravity as an emergent collective
phenomenon from the inflation process itself has the tetrads (AKA
"vierbeins") as the macro-quantum emergent 4D covariant supersolid field
in analogy with the 3D Galilean superfluid velocity field. The tetrad
field is renormalizable spin 1 as a quantum field. Einstein's
geometrodynamic field is quadratic in the tetrad field, therefore any
residual zero point micro-quanta outside of the Bose-Einstein vacuum
ODLRO condensate forming the random anti-gravitating dark energy are
Einstein-Podolsky-Rosen entangled spin 2 triplet pair states of the spin
1 tetrad quanta.

T.W.B. Kibble's 1961 paper "Lorentz Invariance and the Gravitational
Field" JMP 2, March-April 1961 was a marked improvement over Utiyama's
partial solution of the problem that locally gauged only the 6-parameter
homogeneous Lorentz group (AKA Poincare group) to get the spin
connection 1-form w^ab = w^abudx^u for the parallel transport of
orientations of the tetrad 1-forms e^a = e^audx^u, a = 0,1,2,3 AKA
Cartan mobile frames. Utiyama had to stick in the curved metric ad-hoc -
not very satisfactory. Kibble locally gauged the entire 10-parameter
inhomogeneous Lorentz group. This was prior to the elegant math of fiber
bundles in physics where the compensating local gauge potential comes
from the principle bundle and the source fields come from an associated
bundle. Gauge theories use internal symmetry groups G for action
dynamics with the Poincare group as a rigid non-dynamical background
enforcing globally flat spacetime without any gravity at all. The
equivalence principle forces the Poincare group to be dynamical and this
introduces an added layer of complexity, ambiguity and confusion when
trying to cast gravity as a local gauge theory. One must use Dirac's
idea of the "substratum" in which the tetrad fields are well-behaved
spin 1 vector fields when quantized rather than the unrenormalizable
spin 2 tensor fields. It is curious that Kibble, or Penrose later, did
not locally gauge the 15-parameter massless conformal group that is the
basis of twistor theory. Locally gauging the 4-parameter translation
subgroup T4 of the 10-parameter Poincare group gives the Einstein-Cartan
tetrads e^a as the compensating field. However, because of the
equivalence principle, these tetrads are also in the associated bundle
as source fields like the spinor electron field in U(1) QED. That is,
the equivalence principle has a feature like Godel's self-reference. In
a sense this is true of all non-Abelian gauge theories that are
self-interacting forming "geons" or "solitons" or "glue balls" (QCD),
i.e. the gauge field carries the source charge. In the case of gravity
the source charge is stress-energy density. Although the spin 2
geometrodynamic field does not have a local stress-energy tensor, one
cannot jump to that conclusion for the spin 1 tetrad field in the
substratum. Locally gauging the 6-parameter homogeneous group O(1,3)
gives a dynamically independent spin connection. Note, that in
Einstein's 1916 theory, the spin connection is not dynamically
independent. The tetrads are dynamically independent and forcing the
constraint of zero torsion gaps to second order in closed loops of
parallel transport means that the spin connection components are
determined by the tetrad components. This is not so in the general case
treated by Kibble in 1961.

"The extended transformations for which the 10 parameters become
arbitrary functions of position may be interpreted as general coordinate
transformations and rotations of the vierbein system."