  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 Poincare 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.
[file CarlBrans80_07.tex]
