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

  • Friedrich W. HehlEmail author
Part of the Fundamental Theories of Physics book series (FTPH, volume 183)


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 \(\chi ^{ijkl}= -\chi ^{jikl}= -\chi ^{ijlk}\) 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 \(\chi ^{ijkl}\), it can be derived from it.


Maxwell Equation Weyl Group Light Cone Tensor Density Dilaton Field 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This project was partly supported by the German-Israeli Research Foundation (GIF) by the grant GIF/No. 1078-107.14/2009. I am grateful to Claus Kiefer (Cologne) for helpful remarks re Higgs cosmology, to Yuri Obukhov (Moscow) re questions of torsion and of the Hadamard method, to Helmut Rumpf (Vienna) re the Mukhanov bound of \(10^{-29}\,\mathrm{{m}}\), and to Volker Perlick (Bremen) re gravity versus electromagnetism and what is more fundamental. I would like to thank Ari Sihvola and Ismo Lindell (both Espoo/Helsinki) and Alberto Favaro (London) for the permission to use the image in Fig.2. Many useful comments on a draft of this paper were supplied by Hubert Goenner (Göttingen), Yakov Itin (Jerusalem), Claus Lämmerzahl (Bremen), Ecardo Mielke (Mexico City), Wei-Tou Ni (Hsinchu), Erhard Scholz (Wuppertal), Frederic Schuller (Erlangen), and Dirk Puetzfeld (Bremen). I am grateful to Alan Kostelecký (Bloomington) for a last-minute exchange of emails.


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© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Institute for Theoretical PhysicsUniversity of CologneCologneGermany
  2. 2.Department of Physics and AstronomyUniversity of MissouriColumbiaUSA

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