MOND-Like Acceleration in Integrable Weyl Geometric Gravity

Scholz, Erhard

doi:10.1007/s10701-015-9960-z

Cited by 14 publications

(14 citation statements)

References 61 publications

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“…So far this is similar to the well known Jordan-Brans-Dicke (JBD) scalar-tensor theory of gravity [14], [7], [11], [10]. But here we work in a scalar-tensor theory in the framework of Weyl's generalization of Riemannian geometry [2,16,17,22,23]. Crucial for the Weyl geometric scalar tensor approach (WST) is that the scalar curvature R and all dynamical terms involving covariant derivatives are expressed in Weyl geometric scale covariant form.…”

Section: Introductionmentioning

confidence: 68%

“…In this paper the gravitational dynamics of galaxy clusters is investigated from the point of view of Weyl geometric scalar tensor theory of gravity (WST) with a non-quadratic kinematic Lagrange term for the scalar field (3L) similar to the first relativistic MOND theory rAQUAL ("relativistic aquadratic Lagrangian") [23]. To make the paper as self-contained as possible, it starts with an outline of WST-3L (section 1).…”

Section: Introductionmentioning

confidence: 99%

“…because Ω =φ = e ω is the rescaling function from Riemann gauge to scalar field gauge. For more details see [1,6,16,17,23]. For the sake of consistency under rescaling we consider scale covariant geodesics γ(τ ) with scale gauge dependent parametrizations of the geodesic curves of weight w(γ) = −1:…”

Section: Introductionmentioning

confidence: 99%

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Clusters of Galaxies in a Weyl Geometric Approach to Gravity

Scholz

2016

Journal of Gravity

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A model for the dark halos of galaxy clusters, based on the Weyl geometric scalar tensor theory of gravity (WST) with a MOND-like approximation, is proposed. It is uniquely determined by the baryonic mass distribution of hot gas and stars. A first heuristic check against empirical data for 19 clusters (2 of which are outliers), taken from the literature, shows encouraging results. Modulo a caveat resulting from different background theories (Einstein gravity plus ΛCDM versus WST), the total mass for 14 of the outlier reduced ensemble of 17 clusters seems to be predicted correctly (in the sense of overlapping 1 σ error intervals).

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Section: Introductionmentioning

confidence: 68%

Section: Introductionmentioning

confidence: 99%

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Clusters of Galaxies in a Weyl Geometric Approach to Gravity

Scholz

2016

Journal of Gravity

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“…see [59,47] particularly for ϒ k . Thus, if a universal coupling is assumed, then φ should have the intrinsic dilation current ∆ k as its source; for theories in Weyl spaces in which ∆ k does not play a role, see Scholz [87,88].…”

Section: Dilaton Field and Dilation Currentmentioning

confidence: 99%

Axion and Dilaton + Metric Emerge Jointly from an Electromagnetic Model Universe with Local and Linear Response Behavior

Hehl

2016

Fundamental Theories of Physics

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We take a quick look at the different possible universally coupled scalar fields in nature. Then, we discuss how the gauging of the group of scale transformations (dilations), together with the Poincaré group, leads to a Weyl-Cartan spacetime structure. There the dilaton field finds a natural surrounding. Moreover, we describe shortly the phenomenology of the hypothetical axion field. -In the second part of our essay, we consider a spacetime, the structure of which is exclusively specified by the premetric Maxwell equations and a fourth rank electromagnetic response tensor density χ i jkl = −χ jikl = −χ i jlk with 36 independent components. This tensor density incorporates the permittivities, permeabilities, and the magneto-electric moduli of spacetime. No metric, no connection, no further property is prescribed. If we forbid birefringence (double-refraction) in this model of spacetime, we eventually end up with the fields of an axion, a dilaton, and the 10 components of a metric tensor with Lorentz signature. If the dilaton becomes a constant (the vacuum admittance) and the axion field vanishes, we recover the Riemannian spacetime of general relativity theory. Thus, the metric is encapsulated in χ i jkl , it can be derived from it.file CarlBrans80 08.This gauging of the P(1, 3) extends the geometrical framework of gravity. The 4 translational potentials e i α and the 6 Lorentz potentials Γ i αβ = −Γ i β α span a Riemann-Cartan spacetime, enriching the Riemannian spacetime of GR by the presence of Cartan's torsion; here α, β = 0, 1, 2, 3 are (anholonomic) frame indices. Whereas the translational potentials couple to the canonical energy-momentum ten-2 We skip here the plethora of scalar mesons, π ± , π 0 , η, f 0 (500), η ′ (958), f 0 (980), a 0 (980), ...,they are all composed of two quarks. Thus, the scalar mesons do not belong to the fundamental particles.

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“…In this paper, we will analyse the initial value formulation for special types of geometric scalar-tensor theories, which are based on a Weyl integrable structure as a model for spacetime. This type of structures have bee proposed as a suitable model for space-time by several authors [1], [2], [3], [4], [5]. In fact, it is quite interesting that Weyl manifolds appear quite naturally as suitable models for space-time within the well-known axiomatic approach to space-time put forward by Elhers, Pirani and Schild (EPS) in [6].…”

Section: Introductionmentioning

confidence: 99%

On the Cauchy problem for Weyl-geometric scalar-tensor theories of gravity

Avalos¹,

Lobo

Sanomiya

et al. 2018

Journal of Mathematical Physics

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In this paper, we analyse the well-posedness of the initial value formulation for particular kinds of geometric scalar-tensor theories of gravity, which are based on a Weyl integrable space-time. We will show that, within a frame-invariant interpretation for the theory, the Cauchy problem in vacuum is well-posed. We will analyse the global in space problem, and, furthermore, we will show that geometric uniqueness holds for the solutions. We make contact with Brans-Dicke theory, and by analysing the similarities with such models, we highlight how some of our results can be translated to this well-known context, where not all of these problems have been previously addressed.

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MOND-Like Acceleration in Integrable Weyl Geometric Gravity

Cited by 14 publications

References 61 publications

Clusters of Galaxies in a Weyl Geometric Approach to Gravity

Clusters of Galaxies in a Weyl Geometric Approach to Gravity

Axion and Dilaton + Metric Emerge Jointly from an Electromagnetic Model Universe with Local and Linear Response Behavior

On the Cauchy problem for Weyl-geometric scalar-tensor theories of gravity

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