TY - JOUR

T1 - Anisotropic, nonsingular early universe model leading to a realistic cosmology

AU - Dechant, Pierre-Philippe

AU - Lasenby, Anthony

AU - Hobson, Michael

N1 - 2009 The American Physical Society. This is an author produced version of a paper published in Physical Review D. Uploaded in accordance with the publisher's self-archiving policy.

PY - 2009/2/26

Y1 - 2009/2/26

N2 - We present a novel cosmological model in which scalar field matter in a biaxial Bianchi IX geometry leads to a nonsingular “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 quasiregular 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 quasiregular 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 isotropization 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 [ T.¿S. Pereira, C. Pitrou and J.-P. Uzan J. Cosmol. Astropart. Phys. 2007 6 ()][ C. Pitrou, T.¿S. Pereira and J.-P. Uzan J. Cosmol. Astropart. Phys. 2008 4 ()][ A. Gümrükçüoglu, C. Contaldi and M. Peloso J. Cosmol. Astropart. Phys. 2007 005 ()]). 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 generalizes the known bouncing solution in closed FRW universes.

AB - We present a novel cosmological model in which scalar field matter in a biaxial Bianchi IX geometry leads to a nonsingular “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 quasiregular 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 quasiregular 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 isotropization 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 [ T.¿S. Pereira, C. Pitrou and J.-P. Uzan J. Cosmol. Astropart. Phys. 2007 6 ()][ C. Pitrou, T.¿S. Pereira and J.-P. Uzan J. Cosmol. Astropart. Phys. 2008 4 ()][ A. Gümrükçüoglu, C. Contaldi and M. Peloso J. Cosmol. Astropart. Phys. 2007 005 ()]). 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 generalizes the known bouncing solution in closed FRW universes.

UR - http://www.scopus.com/inward/record.url?scp=62549096409&partnerID=8YFLogxK

U2 - 10.1103/PhysRevD.79.043524

DO - 10.1103/PhysRevD.79.043524

M3 - Article

VL - 79

JO - Physical Review D

JF - Physical Review D

SN - 2470-0010

IS - 4

M1 - 043524

ER -