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arXiv · 1205.1474

On the Regularizability of the Big Bang Singularity

Edward Belbruno
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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 $w \leq 1$ 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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Edward Belbruno. 2012-05-02. On the Regularizability of the Big Bang Singularity. https://doi.org/10.1007/s10569-012-9449-4

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