ar X iv : h ep - p h / 06 07 22 9 v 1 2 0 Ju l 2 00 6 Can a vector field be responsible for the curvature perturbation in the Universe ?

I investigate the possibility that the observed curvature perturbation is due to a massive vector field. To avoid generating a large scale anisotropy the vector field is not taken to be driving inflation. Instead it is assumed to become important after inflation when it may dominate the Universe and imprint its perturbation spectrum before its decay, as in the curvaton scenario. It is found that, to generate a scale invariant spectrum of perturbations the mass-squared of the vector field has to be negative and comparable to the Hubble scale during inflation. After inflation the mass-squared must become positive so that the vector field engages into oscillations. It is shown that, such an oscillating vector field behaves as pressureless matter and does not lead to large scale anisotropy when it dominates the Universe. The possibility of realising this scenario in supergravity is also outlined.