2013/02/28 by Hans Westman, H. F. Westman, Tom Złośnik +1
Physics and Astronomy · #Cosmology and Gravitation Theories #Electroweak interaction #Gauge symmetry #Gauge theory #Global symmetry #Higgs boson #Higgs field #Higgs mechanism #Introduction to gauge theory #Noncommutative and Quantum Gravity Theories #Quantum and Classical Electrodynamics #Spontaneous symmetry breaking #Symmetry breaking #gr-qc #hep-th
paper · pdf · doi:10.1088/0264-9381/31/9/095004
2 figures, matches published version
arxiv created 2014/03/24 · openalex publication_date 2014/04/08 · arxiv updated 2015/06/12 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06
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 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 Φ of electroweak theory is taken as a genuine dynamical field satisfying a Klein–Gordon equation, the gauge independent norm V 2 ≡ η 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 = const. ≠ 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 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.