On the Regularizability of the Big Bang Singularity

Abstract

The singularity for the big bang state can be represented using the generalized anisotropic Friedmann equation, resulting in a system of differential equations in a central force field. We study the regularizability of this singularity as a function of a parameter, the equation of state, $w$. We prove that for $w>1$ it is regularizable only for $w$ satisfying relative prime number conditions, and for $w\le 1$ it can always be regularized. This is done by using a McGehee transformation, usually applied in the three and four-body problems. This transformation blows up the singularity into an invariant manifold. The relationship of this result to other cosmological models is briefly discussed.

22 pages, 0 figures

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Cited by in corpus (3)

• Regularization of the big bang singularity with a time varying equation of state $w>1$
• Regularization of the Hill four-body problem with oblate bodies
• Regularization of the big bang singularity with random perturbations