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

Abstract

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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