Inflationary magnetogenesis, derivative couplings and relativistic Van
  der Waals interactions
  When the gauge fields have derivative couplings to scalars, like in the case
of the relativistic theory of Van der Waals (or Casimir-Polder) interactions,
conformal invariance is broken but the magnetic and electric susceptibilities
are not bound to coincide. We analyze the formation of large-scale magnetic
fields in slow-roll inflation and find that they are generated at the level of
a few hundredths of a nG and over typical length scales between few Mpc and
$100$ Mpc. Using a new time parametrization that reduces to conformal time but
only for coincident susceptibilities, the gauge action is quantized while the
evolution equations of the corresponding mode functions are more easily
solvable. The power spectra depend on the normalized rates of variation of the
two susceptibilities (or of the corresponding gauge couplings) and on the
absolute value of their ratio at the beginning of inflation. We pin down
explicit regions in the parameter space where all the physical requirements
(i.e. the backreaction constraints, the magnetogenesis bounds and the
naturalness of the initial conditions of the scenario) are jointly satisfied.
Weakly coupled initial data are favoured if the gauge couplings are of the same
order at the end of inflation. Duality is systematically used to simplify the
analysis of the wide parameter space of the model.
