Paving the way for transitions --- a case for Weyl geometry

Scholz, Erhard

doi:10.48550/arxiv.1206.1559

Cited by 9 publications

(24 citation statements)

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“…34 For the conformal view see, e.g., (Meissner/Nicolai 2009, Bars 2014, for the integrable Weyl geometric one (Nishino/Rajpoot 2011, Nishino/Rajpoot 2007, Quiros 2014, Almeida e.a. 2014, Scholz 2016b, for a non-integrable scale connection (Ohanian 2016).…”

Section: Later Developments and Discussionmentioning

confidence: 99%

Weyl׳s search for a difference between ‘physical’ and ‘mathematical’ automorphisms

Scholz

2018

Studies in History and Philosophy of Science Part B: Studies in

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During his whole scientic life Hermann Weyl was fascinated by the interrelation of physical and mathematical theories. From the mid 1920s onward he reected also on the typical dierence between the two epistemic elds and tried to identify it by comparing their respective automorphism structures. In a talk given at the end of the 1940s (ETH, Hs 91a:31) he gave the most detailed and coherent discussion of his thoughts on this topic. This paper presents his arguments in the talk and puts it in the context of the later development of gauge theories.

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Section: Later Developments and Discussionmentioning

confidence: 99%

Weyl׳s search for a difference between ‘physical’ and ‘mathematical’ automorphisms

Scholz

2018

Studies in History and Philosophy of Science Part B: Studies in

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“…In the sub-indexes '±' and '∓' in ( 61) and ( 62), the upper sign is for the upper half of the phase space while the lower sign is for the lower half. For the EXP (54) the second equation in (62) reads:…”

Section: B Bounded Variables (Bounded Phase Space)mentioning

confidence: 99%

Inflationary equilibrium configurations of scalar-tensor theories of gravity

Quiros,

Gonzalez,

De Arcia

et al. 2020

Preprint

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In this paper we investigate the asymptotic dynamics of inflationary cosmological models that are based in scalar-tensor theories of gravity. Our main aim is to explore the global structure of the phase space in the framework of single-field inflation models. For this purpose we make emphasis in the adequate choice of the variables of the phase space. Our results indicate that, although single-field inflation is generic in the sense that the corresponding critical point in the phase space exists for a wide class of potentials, along given phase space orbits -representing potential cosmic histories -the occurrence of the inflationary stage is rather dependent on the initial conditions. For the non-minimal coupling model with the φ 2 -potential, we have been able to give a rough estimate of the relative probability for initial conditions leading to slow-roll inflation: 10 −13 % < ∼ RP ≪ 10 −8 %. These bonds are greatly improved in the scalar-tensor models, including the Brans-Dicke theory, where the relative probability RP ∼ 50 %. Hence slow-roll inflation is indeed a natural stage of the cosmic expansion in Brans-Dicke models of inflation. We also clarify an issue with the emergence of the ΛCDM cosmological model from the Brans-Dicke theory. It is confirmed as well that the dynamics of vacuum Brans-Dicke theories with arbitrary potentials are non-chaotic.

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“…[9] (see also Refs. [61,62,75,[77][78][79][80][81]). It is linked with the geometrical face of the conformal transformations (1).…”

Section: The (Forgotten) Geometrical Aspect Of Conformal Invariancementioning

confidence: 99%

“…As discussed in section IV, a way out of the above discussed problem may be to look for an appropriate geometrical structure that may really embody the conformal invariance of the action -and of the derived motion equations -of the theory. Here we propose that this geometric structure is a Weyl-integrable manifold (see also [9,32,60,61,75,[78][79][80][81]).…”

Section: Anomaly-free Weyl-invariant Theory Of Gravitymentioning

confidence: 99%

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On local scale invariance and the questionable theoretical basis of the conformal transformations' issue

Quiros,

De Arcia

2018

Preprint

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Here we follow the mainstream of thinking about physical equivalence of different representations of a theory, regarded as the consequence of invariance of the laws of physics -represented by an action principle and the derived motion equations -under given transformations; be it coordinate, gauge or conformal transformations. Accordingly the conformal transformations' issue is discussed by invoking the assumed invariance of the laws of physics -in particular the laws of gravity -under conformal transformations of the metric. It is shown that Brans-Dicke and scalar-tensor theories are not well-suited to address physical equivalence of the conformal frames since the corresponding laws of gravity are not invariant under the conformal transformations or Weyl rescalings. The search for conformal symmetry leads us to explore the physical consequences of Weyl-invariant theories of gravity, that represent a natural arena where to discuss on physical equivalence of the conformally related representations. We show that conformal invariance of the action of a (supposedly conformal invariant) theory and of the derived motion equations is not enough to ensure actual Weyl invariance. It is required, also, that the underlying geometrical structure of the background spacetime be, at least, Weyl-integrable. Otherwise, if assume (as usual) spacetimes of (pseudo)Riemannian geometrical structure, the resulting -apparently conformal invariant -theory is anomalous in that, only massless matter fields can be consistently coupled. Gauge freedom, a distinctive feature of actually Weyl-invariant theories of gravity, leads to very unusual consequences. In a conformal invariant gravity theory over Weyl-integrable spaces, when working within the cosmological setting, an interesting question would not be, for instance, whether the expansion of the universe is accelerating or not, but, which one of the infinitely many physically equivalent conformal universes is the one we live in. It happens, also, that static spherically symmetric black holes are physically equivalent to singularity-free spherically symmetric wormholes. Such apparently senseless consequences in standard scalar-tensor theories, are perfectly allowed in anomaly-free conformal invariant theories of gravity.

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Paving the way for transitions --- a case for Weyl geometry

Cited by 9 publications

References 0 publications

Weyl׳s search for a difference between ‘physical’ and ‘mathematical’ automorphisms

Weyl׳s search for a difference between ‘physical’ and ‘mathematical’ automorphisms

Inflationary equilibrium configurations of scalar-tensor theories of gravity

On local scale invariance and the questionable theoretical basis of the conformal transformations' issue

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