  It has been known for some time that General Relativity can be regarded as a
Yang-Mills-type gauge theory in a symmetry broken phase. In this picture the
gravity sector is described by an $SO(1,4)$ or $SO(2,3)$ gauge field
$A^{a}_{\phantom{a}b\mu}$ and Higgs field $V^{a}$ which acts to break the
symmetry down to that of the Lorentz group $SO(1,3)$. This symmetry breaking
mirrors that of electroweak theory. However, a notable difference is that while
the Higgs field $\Phi$ of electroweak theory is taken as a genuine dynamical
field satisfying a Klein-Gordon equation, the gauge independent norm $V^2\equiv
\eta_{ab}V^{a}V^{b}$ of the Higgs-type field $V^a$ is typically regarded as
non-dynamical. Instead, in many treatments $V^a$ does not appear explicitly in
the formalism or is required to satisfy $V^2 = \mathrm{const.} \neq 0$ by means
of a Lagrangian constraint. As an alternative to this we propose a class of
polynomial actions that treat both the gauge connection
$A^{a}_{\phantom{a}b\mu}$ and Higgs field $V^a$ as genuine dynamical fields
with no ad-hoc constraints imposed. The resultant equations of motion consist
of a set of first-order partial differential equations. We show that for
certain actions these equations may be cast in a second-order form,
corresponding to a scalar-tensor model of gravity. One simple choice leads to
the extensively studied Peebles-Ratra rolling quintessence model. Another
choice yields a scalar-tensor symmetry broken phase of the theory with positive
cosmological constant and an effective mass $M$ of the gravitational Higgs
field ensuring the constancy of $V^2$ at low energies and agreement with
empirical data if $M$ is sufficiently large. More general cases are discussed
corresponding to variants of Chern-Simons modified gravity and scalar-Euler
form gravity, each of which yield propagating torsion.

General Relativity and Quantum Cosmology;High Energy Physics - Theory