  We analyze a massive vector field with a non-canonical kinetic term in the
action, minimally coupled to gravity, where the mass and kinetic function of
the vector field vary as functions of time during inflation. The vector field
is introduced following the same idea of a scalar curvaton, which must not
affect the inflationary dynamics since its energy density during inflation is
negligible compared to the total energy density in the Universe. Using this
hypothesis, the vector curvaton will be solely responsible for generating the
primordial curvature perturbation \zeta. We have found that the spectra of the
vector field perturbations are scale-invariant in superhorizon scales due to
the suitable choice of the time dependence of the kinetic function and the
effective mass during inflation. The preferred direction, generated by the
vector field, makes the spectrum of \zeta depend on the wavevector, i.e. there
exists statistical anisotropy in \zeta. This is discussed principally in the
case where the mass of the vector field increases with time during inflation,
where it is possible to find a heavy field (M >> H) at the end of inflation,
making the particle production be practically isotropic; thus, the longitudinal
and transverse spectra are nearly the same order which in turn causes that the
statistical anisotropy generated by the vector field is within the
observational bounds.
