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

TL;DR

This paper investigates how a fixed-norm spacelike vector field in an anisotropic Bianchi I universe modifies the Jeans instability, leading to direction-dependent growth of density perturbations, with observational constraints on the vector field's vacuum expectation value.

Contribution

It derives the metric for an anisotropic Bianchi I space-time with a vector field and analyzes how this affects the evolution and anisotropy of density perturbations compared to standard models.

Findings

Jeans instability becomes direction-dependent due to the vector field.

The vector field's vacuum expectation value is constrained to be less than approximately 10^{14} GeV.

Anisotropic effects influence the growth of structure in the universe.

Abstract

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, $m \lesssim 10^{14} GeV$.