  Provided the quantum fluctuations are amplified in the presence of a
classical gauge field configuration the resulting curvature perturbations
exhibit a mild statistical anisotropy which should be sufficiently weak not to
conflict with current observational data. The curvature power spectra induced
by weakly anisotropic initial states are computed here for the first time when
the electric and the magnetic gauge couplings evolve at different rates as it
happens, for instance, in the relativistic theory of van der Waals
interactions. After recovering the results valid for coincident gauge
couplings, the constraints imposed by the isotropy and the homogeneity of the
initial states are discussed. The obtained bounds turn out to be more stringent
than naively expected and cannot be ignored when discussing the underlying
magnetogenesis scenarios.
