General Relativity and Gravitation

, Volume 45, Issue 5, pp 1021–1031 | Cite as

Dynamical behaviors of FRW universe containing a positive/negative potential scalar field in loop quantum cosmology

  • Xiao Liu
  • Kui Xiao
  • Jian-Yang Zhu
Research Article


The dynamical behaviors of FRW Universe containing a posivive/negative potential scalar field in loop quantum cosmology scenario are discussed. The method of the phase-plane analysis is used to investigate the stability of the Universe. It is found that the stability properties in this situation are quite different from the classical cosmology case. For a positive potential scalar field coupled with a barotropic fluid, the cosmological autonomous system has five fixed points and one of them is stable if the adiabatic index \(\gamma \) satisfies \(0<\gamma <2\). This leads to the fact that the universe just have one bounce point instead of the singularity which lies in the quantum dominated area and it is caused by the quantum geometry effect. There are four fixed points if one considers a scalar field with a negative potential, but none of them is stable. Therefore, the universe has two kinds of bounce points, one is caused by the quantum geometry effect and the other is caused by the negative potential, the Universe may enter a classical re-collapse after the quantum bounce. This hints that the spatially flat FRW Universe containing a negative potential scalar field is cyclic.


FRW Universe Stability Quantum geometry effect 



This work was supported by the National Natural Science Foundation of China (Grant Nos. 11175019 and 11235003) and Xiao was also supported by the National Natural Science Foundation of China (Grant No. 11247282).


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of PhysicsBeijing Normal UniversityBeijingChina
  2. 2.Department of Basic TeachingHunan Institute of TechnologyHengyangChina

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