Beyond Einstein

Rowe, David E.; Sauer, Tilman; Walter, Scott

doi:10.1007/978-1-4939-7708-6

Cited by 5 publications

(6 citation statements)

References 54 publications

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“…So Einstein-Hilbert action is a "low-energy" limit of Weyl quadratic gravity which thus avoids previous long-held criticisms against it, see e.g. [2]. No additional matter field (scalar, etc) is required.…”

Section: Motivationmentioning

confidence: 84%

“…Introduced a century ago, Weyl's conformal geometry [1][2][3] is a scalar-vector-tensor theory of gravity that is a generalization of Brans-Dicke-Jordan theory of gravity [4]. The latter can be recovered in the limit of vanishing Weyl gauge field.…”

Section: Motivationmentioning

confidence: 99%

“…where F µν is the field strength of the Weyl gauge field ω µ ; it is given by 3 F µν = ∂ µ ω ν − ∂ ν ω µ and is invariant under transformations (1), (2), and the same is true for √ gC µνρσC µνρσ .…”

Section: From Weyl Conformal Geometry To a Riemannian Descriptionmentioning

confidence: 99%

“…Below m ω the Weyl gauge field is absent, so Weyl connection becomes that of the Riemannian geometry,Γ ρ µν = Γ ρ µν . As a result, long-held criticisms of Weyl quadratic gravity without matter [2,17] are avoided: the change of the norm of a vector under parallel transport on a closed curve or the change of the atomic spectral lines spacing under Weyl transformation are effects strongly suppressed by a very high mass scale of Weyl gauge field, m ω ∝ M p .…”

Section: Spontaneous Breaking From Weyl Gauge Symmetry To Einstein Grmentioning

confidence: 99%

“…We consider the SM Higgs field and denote by φ 1 its neutral component. Then the Lagrangian we study, invariant under (1), (2), and written in a Weyl geometry language, is…”

Section: Adding Matter Fields 31 Spontaneous Breaking Of Weyl Gauge mentioning

confidence: 99%

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Spontaneous breaking of Weyl quadratic gravity to Einstein action and Higgs potential

Ghilencea

2019

J. High Energ. Phys.

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We consider the (gauged) Weyl gravity action, quadratic in the scalar curvature (R) and in the Weyl tensor (C µνρσ ) of the Weyl conformal geometry. In the absence of matter fields, this action has spontaneous breaking in which the Weyl gauge field ω µ becomes massive (mass m ω ∼ Planck scale) after "eating" the dilaton in theR 2 term, in a Stueckelberg mechanism. As a result, one recovers the Einstein-Hilbert action with a positive cosmological constant and the Proca action for the massive Weyl gauge field ω µ . Below m ω this field decouples and Weyl geometry becomes Riemannian. The Einstein-Hilbert action is then just a "low-energy" limit of Weyl quadratic gravity which thus avoids its previous, long-held criticisms. In the presence of matter scalar field φ 1 (Higgs-like), with couplings allowed by Weyl gauge symmetry, after its spontaneous breaking one obtains in addition, at low scales, a Higgs potential with spontaneous electroweak symmetry breaking. This is induced by the non-minimal coupling ξ 1 φ 2 1R to Weyl geometry, with Higgs mass ∝ ξ 1 /ξ 0 (ξ 0 is the coefficient of theR 2 term). In realistic models ξ 1 must be classically tuned ξ 1 ≪ ξ 0 . We comment on the quantum stability of this value. *

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Section: Motivationmentioning

confidence: 84%

Section: Motivationmentioning

confidence: 99%

Section: From Weyl Conformal Geometry To a Riemannian Descriptionmentioning

confidence: 99%

Section: Spontaneous Breaking From Weyl Gauge Symmetry To Einstein Grmentioning

confidence: 99%

“…We consider the SM Higgs field and denote by φ 1 its neutral component. Then the Lagrangian we study, invariant under (1), (2), and written in a Weyl geometry language, is…”

Section: Adding Matter Fields 31 Spontaneous Breaking Of Weyl Gauge mentioning

confidence: 99%

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Spontaneous breaking of Weyl quadratic gravity to Einstein action and Higgs potential

Ghilencea

2019

J. High Energ. Phys.

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Asymptotic shear and the intrinsic conformal geometry of null-infinity

Herfray

2020

Journal of Mathematical Physics

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In this article, we propose a new geometrization of the radiative phase space of asymptotically flat space-times: we show that the geometry induced on null-infinity by the presence of gravitational waves can be understood to be a generalization of the tractor calculus of conformal manifolds adapted to the case of degenerate conformal metrics. It follows that the whole formalism is, by construction, manifestly conformally invariant. We first show that a choice of asymptotic shear amounts to a choice of linear differential operator of order 2 on the bundle of scales of null-infinity. We refer to these operators as Poincaré operators. We then show that Poincaré operators are in one-to-one correspondence with a particular class of tractor connections, which we call “null-normal” (they generalize the normal tractor connection of conformal geometry). The tractor curvature encodes the presence of gravitational waves, and the non-uniqueness of flat null-normal tractor connections corresponds to the “degeneracy of gravity vacua” that has been extensively discussed in the literature. This work thus brings back the investigation of the radiative phase space of gravity to the study of (Cartan) connections and associated bundles. This should allow us, in particular, to proliferate invariants of the phase space.

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Classical and quantum fate of the little sibling of the big rip in f(R) cosmology

2019

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The Little Sibling of the Big Rip is a cosmological abrupt event predicted by some phantom cosmological models that could describe our Universe. When this event is approached the observable Universe and its expansion rate grow infinitely, but its cosmic derivative remains finite. In this work we have obtained the group of metric f (R) theories of gravity that reproduce this classical cosmological background evolution. Furthermore, we have considered the quantization of some of the resulting models in the framework of quantum geometrodynamics, showing that the DeWitt criterion can be satisfied. Therefore, as it also happens in General Relativity, this event may be avoided in f (R) quantum cosmology.

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Beyond Einstein

Cited by 5 publications

References 54 publications

Spontaneous breaking of Weyl quadratic gravity to Einstein action and Higgs potential

Spontaneous breaking of Weyl quadratic gravity to Einstein action and Higgs potential

Asymptotic shear and the intrinsic conformal geometry of null-infinity

Classical and quantum fate of the little sibling of the big rip in f(R) cosmology

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