  Particle production of an Abelian vector boson field with an axial coupling
is investigated. The conditions for the generation of scale invariant spectra
for the vector field transverse components are obtained. If the vector field
contributes to the curvature perturbation in the Universe, scale-invariant
particle production enables it to give rise to statistical anisotropy in the
spectrum and bispectrum of cosmological perturbations. The axial coupling
allows particle production to be parity violating, which in turn can generate
parity violating signatures in the bispectrum. The conditions for parity
violation are derived and the observational signatures are obtained in the
context of the vector curvaton paradigm. Two concrete examples are presented
based on realistic particle theory.
