Anisotropic, nonsingular early universe model leading to a realistic cosmology

Abstract

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 [1,2,3]). 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.

Cracking the Taub-NUT

“…For recent work on locally rotationally symmetric (LRS) Bianchi cosmologies with anisotropic matter see, for example, [16]. In [1], we remarked on how Bianchi models can be considered as a deformation of Friedmann-Robertson-Walker (FRW) models, and observed how these perturbations freeze out during inflation. In fact, this can be understood in terms of the characterisation of Bianchi IX models as an FRW model deformed by long range gravitational waves [17].…”

“…We also noted in [1] that, despite containing scalar field matter, our model was reminiscent of the Taub-NUT vacuum solution, since both have biaxial Bianchi IX geometry and an evolution that exhibits a dimensionality reduction at a quasi-regular singularity. In this paper, we show that the metrics for the DLH and Taub-NUT models are, in fact, related by a coordinate transformation.…”

“…As outlined in [1], the Bianchi classification of G 3 group types hinges on the decomposition into irreducible parts of the spatial part of the structure constants C k i j . Imposing the Jacobi identity then essentially leaves nine distinct choices of parameterisations (zeroes and signs) of the structure constants corresponding to nine different groups, called Bianchi I through Bianchi IX.…”

“…In a previous work [1] we argued that it is natural to consider a generalisation of the standard cosmological scenario to one in which a scalar field dominates the dynamics of a homogeneous but, in general, anisotropic (Bianchi) universe. We presented a new solution (the DLH model) to the cosmological field equations based on a closed biaxial Bianchi IX universe containing scalar field matter.…”

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AbstractWe present further analysis of an anisotropic, non-singular early universe model that leads to the viable cosmology presented in [1]. Although this model (the DLH model) contains scalar field matter, it is 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 that one can identify with the big-bang.

We show that the DLH and Taub-NUT metrics are related by a coordinate transformation, in which the DLH time coordinate plays the role of conformal time for Taub-NUT.

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