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Stability analysis of an autonomous system in loop quantum cosmology

Authors :
Xiao, Kui
Zhu, Jian-Yang
Source :
Phys.Rev.D83:083501,2011
Publication Year :
2011

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.<br />Comment: 9 pages

Details

Database :
arXiv
Journal :
Phys.Rev.D83:083501,2011
Publication Type :
Report
Accession number :
edsarx.1102.2695
Document Type :
Working Paper
Full Text :
https://doi.org/10.1103/PhysRevD.83.083501