The Unexpected Resurgence of Weyl Geometry in late 20th-Century Physics

Scholz, Erhard

doi:10.1007/978-1-4939-7708-6_11

Cited by 69 publications

(63 citation statements)

References 233 publications

(279 reference statements)

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“…In this paper we study inflation in a theory with (gauged) local scale invariance. The theory considered is the original Weyl gravity [40][41][42], based on Weyl conformal geometry [43]. This symmetry is also referred to as Weyl gauge symmetry and its associated gauge boson is called hereafter Weyl "photon".…”

Section: Motivationmentioning

confidence: 99%

Weyl R2 inflation with an emergent Planck scale

Ghilencea

2019

J. High Energ. Phys.

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We study inflation in Weyl gravity. The original Weyl quadratic gravity, based on Weyl conformal geometry, is a theory invariant under Weyl symmetry of (gauged) local scale transformations. In this theory Planck scale (M ) emerges as the scale where this symmetry is broken spontaneously by a geometric Stueckelberg mechanism, to Einstein-Proca action for the Weyl "photon" (of mass near M ). With this action as a "low energy" broken phase of Weyl gravity, long-held criticisms of the latter (due to non-metricity) are avoided. In this context, inflation with field values above M is natural, since this is just a phase transition scale from Weyl gravity (geometry) to Einstein gravity (Riemannian geometry), where the massive Weyl photon decouples. We show that inflation in Weyl gravity coupled to a scalar field has results close to those in Starobinsky model (recovered for vanishing non-minimal coupling), with a mildly smaller tensor-to-scalar ratio (r). Weyl gravity predicts a specific, narrow range 0.00257 ≤ r ≤ 0.00303, for a spectral index n s within experimental bounds at 68%CL and e-folds number N = 60. This range of values will soon be reached by CMB experiments and provides a test of Weyl

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Section: Motivationmentioning

confidence: 99%

Weyl R2 inflation with an emergent Planck scale

Ghilencea

2019

J. High Energ. Phys.

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“…Weyl-squared gravity (see, e.g., [110] for a review) is in some sense the exact opposite of unimodular gravity: Whereas the latter features a fixed, non-dynamical conformal factor, the former declares conformal/Weyl transformations (i.e., rescaling of the metric by a local conformal factor, g µν → Ω 2 (x)g µν ) to be gauge transformations. This enhanced symmetry strongly constrains the viable dynamics.…”

Section: Introduction To (Unimodular) Asymptotically Safe Gravitymentioning

confidence: 99%

A link that matters: towards phenomenological tests of unimodular asymptotic safety

Brito

Eichhorn

Pereira

2019

J. High Energ. Phys.

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Constraining quantum gravity from observations is a challenge. We expand on the idea that the interplay of quantum gravity with matter could be key to meeting this challenge.Thus, we set out to confront different potential candidates for quantum gravity -unimodular asymptotic safety, Weyl-squared gravity and asymptotically safe gravity -with constraints arising from demanding an ultraviolet complete Standard Model. Specifically, we show that within approximations, demanding that quantum gravity solves the Landau-pole problems in Abelian gauge couplings and Yukawa couplings strongly constrains the viable gravitational parameter space. In the case of Weyl-squared gravity with a dimensionless gravitational coupling, we also investigate whether the gravitational contribution to beta functions in the matter sector calculated from functional Renormalization Group techniques is universal, by studying the dependence on the regulator, metric field parameterization and choice of gauge. I. INTRODUCTIONObservational constraints on quantum gravity are hard to come by. Based on a simple dimensional argument, one typically expects a power-law suppression of quantum-gravity effects 1 with (E/M Pl ) # , with E being the energy scale relevant for experiments, M Pl being the Planck mass and # > 0. Nevertheless, mathematical and internal consistency are not the only conditions that could * Electronic address: gpbrito@cbpf.br † Electronic address: eichhorn@sdu.dk ‡ Electronic address: adpjunior@id.uff.br 1 In the presence of a second "meso"-scale, as hinted at by some quantum-gravity approaches, e.g., [1], this situation can change.

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“…In the most of these works, including ours, the Weyl interpretation is considered as the geometric component of the physical theory, see the extensive review by [37]. The Weylian metric on a differentiable manifold M (in Ref.…”

Section: Introduction To the Original Theorymentioning

confidence: 99%

“…Examples are: W(g µν ) = 2, W(g µν ) = −2 etc. A theory or an expression invariant under this transformation is called conformally invariant, or is said to possess Weyl invariance or Weyl symmetry.Jordan-Brans-Dicke (JBD) theory assumes a scalar field χ of scale weight W(χ) = −1, coupled to gravity (a pseudo-Riemannian metric g) by a Lagrangian of the following type[37] …”

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confidence: 99%

The Ambiguity in the Definition and Behavior of the Gravitational and Cosmological ‘Coupling Constants’ in the Theory of Induced Gravity

Zaripov¹

2019

Symmetry

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This work is the extension of author's research, where the modified theory of induced gravity (MTIG) is proposed. The theory describes two systems (stages): Einstein (ES) and "restructuring" (RS). We consider equations with quadratic potential that are symmetric with respect to scale transformations. The solutions of the equations obtained for the case of spaces defined by the Friedman-Robertson-Walker metric, as well as for a centrally symmetric space are investigated. In our model arise effective gravitational and cosmological "constants" , which are defined by the "mean square" of the scalar fields. In obtained solutions the values of such parameters as "Hubble parameter", gravitational and cosmological "constants" in the RS stage fluctuate near monotonically evolving mean values. These parameters are matched with observational data, described as phenomena of dark energy and dark matter. The MTIG equations for the case of a centrally symmetric gravitational field, in addition to the Schwarzschild-de Sitter solutions, contain solutions that lead to the new physical effects at large distances from the center. The Schwarzschild-Sitter solution becomes unstable and enters the oscillatory regime. For distances greater than a certain critical value, the following effects can appear: deviation from General relativity and Newton's law of gravitational interaction, antigravity. Telescope (HST) and Planck observatory [5]. The Hubble Space Telescope is tuned to measure the parallax Milky Way Cepheid variables and the distances are 1.7-3.6 kpc (the modern Universe). The measurements of the Planck spacecraft correspond to distant galaxies (the early Universe is about 375,000 years old). In 2018, the accuracy of the measurement of H 0 is increased to 2.3 percent, which gives H 0 = 73.48 ± 1.66 km · s −1 Mpc −1 . In the early Universe, based on the data received from the "Planck" spacecraft and ΛCDM theory, the predicted value is H 0 = 67.0 ± 1.2 km · s −1 Mpc −1 . The difference is about 9 percent. The accuracy of the measurements is about 4.5 percent. There is also a variance in the observations made at different times and different methods. For example, as indicated in the work [6], the local and direct definition of H 0 gives H 0 = 73.24 ± 1.74 km · s −1 Mpc −1 , and the most recent value from [7] in consent with ΛCDM is 66.93 ± 0.62 km · s −1 Mpc −1 . In our opinion, the problem can be reduced to a strong binding of calculations of the Hubble parameter H 0 to the ΛCDM model. In our work we present a model where, due to the oscillatory regime in the solutions of equations, the Hubble parameter also fluctuates with respect to the mean value-which is also a function of time.3. The problems of so-called "dark energy" (DE) and "dark matter" (DM). The first of them can be reduced to the problem of existence and smallness of the "cosmological constant" (par. 1). The challenge posed by the cosmological constant problem [1] has spurred many attempts at directly modifying Einstein's gravity at large distances [8]. As example of s...

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The Unexpected Resurgence of Weyl Geometry in late 20th-Century Physics

Cited by 69 publications

References 233 publications

Weyl R2 inflation with an emergent Planck scale

Weyl R2 inflation with an emergent Planck scale

A link that matters: towards phenomenological tests of unimodular asymptotic safety

The Ambiguity in the Definition and Behavior of the Gravitational and Cosmological ‘Coupling Constants’ in the Theory of Induced Gravity

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