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An introduction to the physics of Cartan gravity

AuthorsWestman, H.F.; Zlosnik, T.G.
Modified gravity
Issue Date8-Jul-2015
CitationAnnals of Physics 361: 330- 376 (2015)
Abstract© 2015 Elsevier Inc.. A distance can be measured by monitoring how much a wheel has rotated when rolled without slipping. This simple idea underlies the mathematics of Cartan geometry. The Cartan-geometric description of gravity consists of a SO(1, 4) gauge connection A AB(x) and a gravitational Higgs field V A (x) which breaks the gauge symmetry. The clear similarity with symmetry-broken Yang–Mills theory suggests strongly the existence of a new field V A in nature: the gravitational Higgs field. By treating V A as a genuine dynamical field we arrive at a natural generalization of General Relativity with a wealth of new phenomenology. Importantly, General Relativity is reproduced exactly in the limit that the SO(1, 4) norm V 2 (x) tends to a positive constant. We show that in regions wherein V 2 varies – but has a definite sign – the Cartan-geometric formulation is a particular version of a scalar–tensor theory (in the sense of gravity being described by a scalar field φ, metric tensor gµν , and possibly a torsion tensor Tµν ρ ). A specific choice of action yields the Peebles–Ratra quintessence model whilst more general actions are shown to exhibit propagation of torsion. Regions where the sign of V 2 changes correspond to a change in signature of the geometry. Specifically, a simple choice of action with FRW symmetry imposed yields, without any additional ad hoc assumptions, a classical analogue of the Hartle–Hawking no-boundary proposal with the big bang singularity replaced by signature change. Cosmological solutions from more general actions are described, none of which have a big bang singularity, with most solutions reproducing General Relativity, or its Euclidean version, for late cosmological times. Requiring that gravity couples to matter fields through the gauge prescription forces a fundamental change in the description of bosonic matter fields: the equations of motion of all matter fields become first-order partial differential equations with the scalar and Dirac actions taking on structurally similar first-order forms. All matter actions reduce to the standard ones in the limit V 2 → const. We argue that Cartan geometry may function as a novel platform for inspiring and exploring modified theories of gravity with applications to dark energy, black holes, and early-universe cosmology. We end by listing a set of open problems.
Description47 págs.; 11 figs.; 5 apps.
Publisher version (URL)http://dx.doi.,org/10.1016/j.aop.2015.06.013
Identifiersdoi: 10.1016/j.aop.2015.06.013
issn: 1096-035X
Appears in Collections:(CFMAC-IFF) Artículos
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