Exploring Cartan gravity with dynamical symmetry breaking

Westman, Hans; Złośnik, Tom

doi:10.1088/0264-9381/31/9/095004

Cited by 14 publications

(32 citation statements)

References 52 publications

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“…By recasting the equation for V 2 into a second order form we see that a viscous term appears and this suggests that the constancy of V 2 is caused by 'friction' causing the velocity |dV 2 /dτ | to decrease. Note that this mechanism is entirely distinct from the mechanism discovered in [41] wherein it was found that certain combinations of {ai, bi, ci} terms in the action were equivalent to a scalar-tensor theory equipped with a potential with stable minimum at non-zero V 2 . We leave it for future investigations to determine whether the former, new symmetry breaking mechanism also works outside the cosmological framework developed in this paper.…”

Section: Discussionmentioning

confidence: 78%

Cosmological signature change in Cartan gravity with dynamical symmetry breaking

et al. 2014

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We investigate the possibility for classical metric signature change in a straightforward generalization of the first-order formulation of gravity, dubbed "Cartan gravity." The mathematical structure of this theory mimics the electroweak theory in that the basic ingredients are an SOð1; 4Þ Yang-Mills 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 SOð1; 3Þ 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 four-metric. These solutions are nonsingular and arise whenever the SOð1; 4Þ 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 well-known dark energy model: Peebles-Ratra quintessence.

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Section: Discussionmentioning

confidence: 78%

Cosmological signature change in Cartan gravity with dynamical symmetry breaking

et al. 2014

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“…Other papers on extended MacDowell-Mansouri formalism include: An interesting paper [129] studying Stelle-West-type actions with a potential term for the compensator field instead of the Lagrange multiplier term. It is shown that the result is a variant of scalar-tensor theory of gravity.…”

Section: Macdowell-mansouri Type Unificationmentioning

confidence: 99%

Gravity and unification: a review

Krasnov

Percacci

2018

Class. Quantum Grav.

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We review various classical unified theories of gravity and other interactions that have appeared in the literature, paying special attention to scenarios in which spacetime remains four-dimensional, while an "internal" space is enlarged. The starting point for each such unification scenario is a particular formalism for General Relativity. We thus start by reviewing, besides the usual Einstein-Hilbert and Palatini formulations, the Einstein-Cartan, MacDowell-Mansouri and BF (both nonchiral and chiral) formulations. Each of these introduces some version of "internal" bundle and a dynamical variable that ties the internal and tangent bundles. In each of these formulations there is also an independent connection in the "internal" bundle. One can then study the effects of "enlarging the internal space", which typically leads to a theory of gravity and Yang-Mills fields.We review what has been done in the literature on each of these unification schemes, and compare and contrast their achievements to those of the better developed Kaluza-Klein scenario. * Electronic address: kirill.krasnov@nottingham.ac.uk † Electronic address: percacci@sissa.it

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“…The complication introduced by the a 1 and a 3 terms (only if a 3 depends on φ 2 ) is that spacetime gradients of φ can also couple to derivatives of C IJ in the C IJ equation of motion, hence in this case C IJ cannot generally be solved for algebraically in terms of e I and φ (and derivatives thereof) and hence eliminated from the variational principle. Specifically, such terms are [11]:…”

Section: Propagating Torsionmentioning

confidence: 99%

An introduction to the physics of Cartan gravity

Westman

Złośnik

2015

Annals of Physics

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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.

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Exploring Cartan gravity with dynamical symmetry breaking

Cited by 14 publications

References 52 publications

Cosmological signature change in Cartan gravity with dynamical symmetry breaking

Cosmological signature change in Cartan gravity with dynamical symmetry breaking

Gravity and unification: a review

An introduction to the physics of Cartan gravity

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