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arXiv · 1102.2695

Stability analysis of an autonomous system in loop quantum cosmology

Kui Xiao·Jian-Yang Zhu
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Abstract

We discuss the stability properties of an autonomous system in loop quantum cosmology. The system is described by a self-interacting scalar field $\phi$ with positive potential $V$, coupled with a barotropic fluid in the Universe. With $\Gamma=VV"/V'^2$ considered as a function of $\lambda=V'/V$, the autonomous system is extended from three dimensions to four dimensions. We find that the dynamic behaviors of a subset, not all, of the fixed points are independent of the form of the potential. Considering the higher-order derivatives of the potential, we get an infinite-dimensional autonomous system which can describe the dynamical behavior of the scalar field with more general potential. We find that there is just one scalar-field-dominated scaling solution in the loop quantum cosmology scenario.

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Kui Xiao, Jian-Yang Zhu. 2011-02-14. Stability analysis of an autonomous system in loop quantum cosmology. https://doi.org/10.1103/physrevd.83.083501

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