An anisotropic, non-singular early universe model leading to a realistic   cosmology
  We present a novel cosmological model in which scalar field matter in a biaxial Bianchi IX geometry leads to a non-singular `pancaking' solution: the hypersurface volume goes to zero instantaneously at the `Big Bang', but all physical quantities, such as curvature invariants and the matter energy density remain finite, and continue smoothly through the Big Bang. We demonstrate that there exist geodesics extending through the Big Bang, but that there are also incomplete geodesics that spiral infinitely around a topologically closed spatial dimension at the Big Bang, rendering it, at worst, a quasi-regular singularity. The model is thus reminiscent of the Taub-NUT vacuum solution in that it has biaxial Bianchi IX geometry and its evolution exhibits a dimensionality reduction at a quasi-regular singularity; the two models are, however, rather different, as we will show in a future work. Here we concentrate on the cosmological implications of our model and show how the scalar field drives both isotropisation and inflation, thus raising the question of whether structure on the largest scales was laid down at a time when the universe was still oblate (as also suggested by Pitrou et al and Contaldi et al). We also discuss the stability of our model to small perturbations around biaxiality and draw an analogy with cosmological perturbations. We conclude by presenting a separate, bouncing solution, which generalises the known bouncing solution in closed FRW universes. 
Pierre-Philippe Dechant, Anthony N. Lasenby, Michael P. Hobson