Weyl geometric gravity and electroweak symmetry “breaking”

Scholz, Erhard

doi:10.1002/andp.201100032

Cited by 14 publications

(18 citation statements)

References 55 publications

(156 reference statements)

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“…The variation of L φ gives a peculiar energy-momentum contribution from the scalar field to the r.h.s. (see below, (47), (48)). We arrive at the scale invariant Einstein equation,…”

Section: Dynamical Equationsmentioning

confidence: 99%

“…In vacuum the r.h.s. of the Einstein equation (47,48) simplifies to the quartic term ("cosmological constant") of the scalar field potential (49):…”

Section: Schwarzschild-de Sitter Solutionmentioning

confidence: 99%

“…The energy-momentum tensor of the scalar field T (φ) . = (8πG) −1 Θ is given by (47), (48). Because of ∂ o ω = 0 the second 34 [44,46].…”

Section: Scalar Field Energy Densitymentioning

confidence: 99%

“…For more details see, among many others,[1,7,36,37,47] from the point of view of physics, for a differential geometric perspective[21,27,24]. 5[27,9,34,24] 6.…”

mentioning

confidence: 99%

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MOND-Like Acceleration in Integrable Weyl Geometric Gravity

Scholz

2015

Found Phys

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In this paper a Weyl geometric scalar tensor theory of gravity with scalar field φ and scale invariant cubic ("aquadratic") kinetic Lagrangian is introduced. Einstein gauge (comparable to Einstein frame in Jordan-Brans-Dicke theory) is most natural for studying trajectories. In it, the Weylian scale connection induces an additional acceleration which in the weak field, static, low velocity limit acquires the deep MOND form of Milgrom/Bekenstein's gravity. The energy momentum of φ leads to another add on to Newton acceleration. Both additional accelerations together imply a MOND-ian phenomenology of the model. It has unusual transition functions µ w (x), ν w (y). They imply higher phantom energy density than in the case of the more common MOND models with transition functions µ 1 (x), µ 2 (x). A considerable part of it is due to the scalar field's energy density which, in our model, gives a scale and generally covariant expression for the self-energy of the gravitational field.

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“…The variation of L φ gives a peculiar energy-momentum contribution from the scalar field to the r.h.s. (see below, (47), (48)). We arrive at the scale invariant Einstein equation,…”

Section: Dynamical Equationsmentioning

confidence: 99%

“…In vacuum the r.h.s. of the Einstein equation (47,48) simplifies to the quartic term ("cosmological constant") of the scalar field potential (49):…”

Section: Schwarzschild-de Sitter Solutionmentioning

confidence: 99%

“…The energy-momentum tensor of the scalar field T (φ) . = (8πG) −1 Θ is given by (47), (48). Because of ∂ o ω = 0 the second 34 [44,46].…”

Section: Scalar Field Energy Densitymentioning

confidence: 99%

“…For more details see, among many others,[1,7,36,37,47] from the point of view of physics, for a differential geometric perspective[21,27,24]. 5[27,9,34,24] 6.…”

mentioning

confidence: 99%

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MOND-Like Acceleration in Integrable Weyl Geometric Gravity

Scholz

2015

Found Phys

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“…Moreover, the generalized Ricci tensor and scalar in metric measure space, relations (3) and (4), will be the same as those in integrable Weyl space, relations (36) and (37), provided that s 1 = 0. In other words, assuming (44) and s 1 = 0, (or equivalently s 2 =-2), leads to…”

Section: Comparing With Metric Measure Spacementioning

confidence: 99%

A conformally invariant theory of gravitation in metric measure space

Rahmanpour

Shojaie

2015

Gen Relativ Gravit

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In this manuscript, a conformally invariant theory of gravitation in the context of metric measure space is studied. The proposed action is invariant under both diffeomorphism and conformal transformations. Using the variational method, a generalization of the Einstein equation is obtained, wherein the conventional tensors are replaced by their conformally invariant counterparts, living in metric measure space. The invariance of the geometrical part of the action under a diffeomorphism leads to a generalized contracted second Bianchi identity. In metric measure space, the covariant derivative is the same as it is in the Riemannian space. Hence, in contrast to the Weyl space, the metricity and integrability are maintained. However, it is worth noting that in metric measure space the divergence of a tensor is not simply the contraction of the covariant derivative operator with the tensor that it acts on. Despite the fact that metric measure space and integrable Weyl space, are constructed based on different assumptions, it is shown that some relations in these spaces, such as the contracted second Bianchi identity, are completely similar.

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Paving the Way for Transitions—A Case for Weyl Geometry

Scholz

2017

Towards a Theory of Spacetime Theories

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This paper presents three aspects by which the Weyl geometric generalization of Riemannian geometry, and of Einstein gravity, sheds light on actual questions of physics and its philosophical reflection. After introducing the theory's principles, it explains how Weyl geometric gravity relates to Jordan-Brans-Dicke theory. We then discuss the link between gravity and the electroweak sector of elementary particle physics, as it looks from the Weyl geometric perspective. Weyl's hypothesis of a preferred scale gauge, setting Weyl scalar curvature to a constant, gets new support from the interplay of the gravitational scalar field and the electroweak one (the Higgs field). This has surprising consequences for cosmological models. In particular it leads to a static (Weyl geometric) spacetime with "inbuilt" cosmological redshift. This may be used for putting central features of the present cosmological model into a wider perspective.

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Weyl geometric gravity and electroweak symmetry “breaking”

Cited by 14 publications

References 55 publications

MOND-Like Acceleration in Integrable Weyl Geometric Gravity

MOND-Like Acceleration in Integrable Weyl Geometric Gravity

A conformally invariant theory of gravitation in metric measure space

Paving the Way for Transitions—A Case for Weyl Geometry

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