H. F. Westman, T. G. Zlosnik
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 $A^{a}_{\ph{a}b\mu}$ 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 component $V^2$ 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 $V^2\equiv \eta_{ab}V^{a}V^{b}=const.$ by means of a Lagrangian constraint. As an alternative to this we propose a class of polynomial actions that treat both the gauge connection $A^{a}_{\ph{a}b\mu}$ and Higgs field $V^a$ as genuine dynamical fields. 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. A specific choice based on the symmetry group SO(1,4) yields a 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 actions are discussed corresponding to variants of Chern-Simons modified gravity and scalar-Euler form gravity.
View original:
http://arxiv.org/abs/1302.1103
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