摘要For the variable generalized Chaplygin gas (VGCG) as a dynamical system, its stability is analyzed and the related dynamical attractors are investigated. By analysis it is shown that there are two critical points corresponding to the matter-dominated phase and the VGCG dark energy-dominated phase, respectively. Moreover, when the parameters n, α and γ take some fixed values, the phase with ωVGCG= -0.92 is a dynamical attractor and the equation of state of VGCG reaches it from either ωVGCG > -1 or ωVGCG< -1, independent of the initial values of the dynamical system. This shows a satisfactory cosmological model: the early matter-dominated era, followed by the dark energy-dominated era. Meanwhile, the evolutions of density parameters Ωγ and ΩVGCG are quite different from each other. For different initial values of x and y,Ωγ decreases and ΩVGCG increases as the time grows, they will eventually approach Ωγ=0 and ΩVGCG= 1. Furthermore, since different values of n or α may lead to different equation-of-state parameters ΩVGCG, we also discuss the constraints on the parameters n and α by the observation data.
Abstract：For the variable generalized Chaplygin gas (VGCG) as a dynamical system, its stability is analyzed and the related dynamical attractors are investigated. By analysis it is shown that there are two critical points corresponding to the matter-dominated phase and the VGCG dark energy-dominated phase, respectively. Moreover, when the parameters n, α and γ take some fixed values, the phase with ωVGCG= -0.92 is a dynamical attractor and the equation of state of VGCG reaches it from either ωVGCG > -1 or ωVGCG< -1, independent of the initial values of the dynamical system. This shows a satisfactory cosmological model: the early matter-dominated era, followed by the dark energy-dominated era. Meanwhile, the evolutions of density parameters Ωγ and ΩVGCG are quite different from each other. For different initial values of x and y,Ωγ decreases and ΩVGCG increases as the time grows, they will eventually approach Ωγ=0 and ΩVGCG= 1. Furthermore, since different values of n or α may lead to different equation-of-state parameters ΩVGCG, we also discuss the constraints on the parameters n and α by the observation data.
(Mathematical and relativistic aspects of cosmology)
引用本文:
FU Huan-Huan;WU Ya-Bo;CHENG Fang-Yuan. Dynamical Stability and Attractor of the Variable Generalized Chaplygin Gas Model[J]. 中国物理快报, 2009, 26(6): 69801-069801.
FU Huan-Huan, WU Ya-Bo, CHENG Fang-Yuan. Dynamical Stability and Attractor of the Variable Generalized Chaplygin Gas Model. Chin. Phys. Lett., 2009, 26(6): 69801-069801.
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2009, Vol. 26 
