Direction-dependent Jeans instability in an anisotropic Bianchi type I space-time

We derive the metric for a Bianchi type I space-time with energy density that is dominated by that of a perfect fluid with equation of state $p=w\rho$ and whose anisotropy is seeded by a fixed norm spacelike vector field. We solve for the evolution of perturbations about this space-time. In particular, the Jeans instability in an expanding flat Friedmann-Robertson-Walker universe is modified by the presence of the vector field so that energy density perturbations develop direction-dependent growth. We also briefly consider observational limits on the vector field vacuum expectation value, $m$. We find that, if $m$ is constant during recombination and thereafter, $m \lesssim 10^{14} GeV$.