Stability analysis of an autonomous system in loop quantum cosmology

Details Stability analysis of an autonomous system in loop quantum cosmology Stability analysis of an autonomous system in loop quantum cosmology

2011-02-14

arxiv.org/abs/1102.2695v2

Phys.Rev.D83:083501,2011

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

9 pages

Scientific paper

10.1103/PhysRevD.83.083501

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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