Timelike Vector Field Dynamics in the Early Universe

Abstract

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 $\xi =1/6$.

Comments: 16pages, 4 figures, corrected equation (6), added references v3: added references and comments, v4: extended sec. III