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arXiv · 1809.09659

A quantum gravity extension to the Mixmaster dynamics

Edward Wilson-Ewing
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Abstract

In the loop quantum cosmology effective dynamics for the vacuum Bianchi type I and type IX space-times, a non-singular bounce replaces the classical singularity. The bounce can be approximated as an instantaneous transition between two classical vacuum Bianchi I solutions, with simple transition rules relating the solutions before and after the bounce. These transition rules are especially simple when expressed in terms of the Misner variables: the evolution of the mean logarithmic scale factor is reversed, while the shape parameters are unaffected. As a result, the loop quantum cosmology effective dynamics for the vacuum Bianchi IX space-time can be approximated by a sequence of classical vacuum Bianchi I solutions, following the usual Mixmaster transition maps in the classical regime, and undergoing a bounce with this new transition rule in the Planck regime.

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Edward Wilson-Ewing. 2018-09-25. A quantum gravity extension to the Mixmaster dynamics. https://doi.org/10.1088/1361-6382%2Fab392b

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