Cosmological signature change in Cartan gravity with dynamical symmetry breaking
Abstract
We investigate the possibility for classical metric signature change in a straightforward generalization of the firstorder formulation of gravity, dubbed "Cartan gravity." The mathematical structure of this theory mimics the electroweak theory in that the basic ingredients are an SO(1,4) YangMills gauge field A^{ab}μ and a symmetry breaking Higgs field V^{a}, with no metric or affine structure of spacetime presupposed. However, these structures can be recovered, with the predictions of general relativity exactly reproduced, whenever the Higgs field breaking the symmetry to SO(1,3) is forced to have a constant (positive) norm V^{a}V_{a}. This restriction is usually imposed "by hand," but in analogy with the electroweak theory we promote the gravitational Higgs field V^{a} to a genuine dynamical field, subject to nontrivial equations of motion. Even though we limit ourselves to actions polynomial in these variables, we discover a rich phenomenology. Most notably we derive classical cosmological solutions exhibiting a smooth transition between Euclidean and Lorentzian signature in the fourmetric. These solutions are nonsingular and arise whenever the SO(1,4) norm of the Higgs field changes sign; i.e. the signature of the metric of spacetime is determined dynamically by the gravitational Higgs field. It is possible to find a plethora of such solutions and in some of them this dramatic behavior is confined to the early Universe, with the theory asymptotically tending to Einstein gravity at late times. Curiously the theory can also naturally embody a wellknown dark energy model: PeeblesRatra quintessence.
 Publication:

Physical Review D
 Pub Date:
 March 2014
 DOI:
 10.1103/PhysRevD.89.063542
 arXiv:
 arXiv:1311.4481
 Bibcode:
 2014PhRvD..89f3542M
 Keywords:

 04.50.Kd;
 Modified theories of gravity;
 General Relativity and Quantum Cosmology;
 Astrophysics  Cosmology and Nongalactic Astrophysics
 EPrint:
 Matches published version