Mixmaster Fluids Near the Big Bang

Abstract

We numerically study the approach to the singularity in ${\mathbb{T}}^2$-symmetric cosmological spacetimes containing a non-stiff perfect fluid satisfying a linear equation of state $p=K\ddot{I}$, $K\in [0,1)$. Near the singularity, the dynamics are found to be local and oscillatory. In particular, our results show, for the first time, that the fluid velocity in inhomogeneous cosmologies develops mixmaster-esque oscillations consistent with the generalised BKL conjecture of Uggla et al. Moreover, we find these fluid oscillations are responsible for the development of local inhomogeneities in the matter density of the early universe.

Material added to address referee comments, discussion of equations condensed, appendices removed. Agrees with published version. 22 pages, 10 figures. v3: Minor typos corrected