Particle Production of Vector Fields: Scale Invariance is Attractive
  In a model of an Abelian vector boson with a Maxwell kinetic term and
non-negative mass-squared it is demonstrated that, under fairly general
conditions during inflation, a scale-invariant spectrum of perturbations for
the components of a vector field, massive or not, whose kinetic function (and
mass) is modulated by the inflaton field is an attractor solution. If the field
is massless, or if it remains light until the end of inflation, this attractor
solution also generates anisotropic stress, which can render inflation weakly
anisotropic. The above two characteristics of the attractor solution can source
(independently or combined together) significant statistical anisotropy in the
curvature perturbation, which may well be observable in the near future.
