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 ≤ 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.
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Belbruno, E. On the regularizability of the big bang singularity. Celest Mech Dyn Astr 115, 21–34 (2013). https://doi.org/10.1007/s10569-012-9449-4
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DOI: https://doi.org/10.1007/s10569-012-9449-4