  We study the dynamics of a timelike vector field which violates Lorentz
invariance when the background spacetime is in an accelerating phase in the
early universe. It is shown that a timelike vector field is difficult to
realize an inflationary phase, so we investigate the evolution of a vector
field within a scalar field driven inflation model. And we calculate the power
spectrum of the vector field without considering the metric perturbations.
While the time component of the vector field perturbations provides a scale
invariant spectrum when $\xi = 0$, where $\xi$ is a nonminimal coupling
parameter, both the longitudinal and transverse perturbations give a scale
invariant spectrum when $\xi = 1/6$.
