耦合为αHρ_φ+βHρ_m的k-essence暗能量模型相空间分析

Phase-space Analysis of K-essence Dark Energy Model with the Coupling αHρ_φ+βHρ_m

结合最近十年宇宙学中关于k-essence暗能量模型的多篇论文观点,本文适当选取F(X)=-X(1/2)+X构造拉格朗日量,同时尝试改进暗物质与暗能量的非零相互耦合0≠Q=αHρ_φ+βHρ_m,使其既与暗物质相关又与暗能量相关。进而推导出更普遍的相空间演化自洽微分方程组。最后在满足宇宙加速膨胀这一观测结果的前提下,设定参数α,β,λ的数值,并作出相空间演化图,标记出相空间演化的稳定点,定性地分析出宇宙演化晚期的几种可能结果。

With the views from the papers for the last ten years about k-essence dark energy models, this paper chooses F（X） = - √X ＋ X to make the Lagrangian, and tries the coupling term 0≠Q=αHρφ＋βHρm between dark matter and dark energy, and it derives the general self-contain evolution differential equations. Finally, under the observation fact of accelerating expansion, three parameters α,β,λ are set to draw the phase-space evolution pictures, and the stable points, including the critical points, are marked on the pictures to demonstrate the possible result of the late cosmology dynamical evolution.