标量场模型非线性行为研究

项目名称： 标量场模型非线性行为研究

项目编号： No.11263003

项目类型： 地区科学基金项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 马大柱

作者单位： 湖北民族学院

项目金额： 45万元

中文摘要： 观测表明，当前宇宙正在加速膨胀。标量场作为暗能量的候选提供了宇宙加速膨胀的依据，已经成为热门研究领域。准确反映标量场暗能量模型的非线性演化过程取决于两个必要条件，一是较为理想的模型，二是可靠的混沌识别方法。基于以上两个条件的考虑，课题组拟以共形耦合标量场模型和各向异性的暴涨模型为基本研究模型，首先通过数值实验对比研究流形改正方案和辛算法，讨论在平直时空广泛应用的混沌识别指标。然后对灵敏度较高的算法改造后应用到弯曲时空中去。最后深入讨论标量场模型非线性行为，讨论参数的变化所产生的混沌动力学特征。为宇宙加速膨胀提供更多理论依据。

中文关键词： 标量场；混沌指标；弦；保守系统；耗散系统

英文摘要： So far, there has been convincing observational evidence that the universe is currently in a phase of accelerated expansion. Scalar field which acts as a candidate for dark energy provides the evidence for the accelerated expansion of the universe, and it becomes a hot topic now. It depends on two necessary conditions to reflect accurately nonlinear behavior of the scalar field dark energy model. One is idealized model, the other is reliable method which is used to detect chaos. In view of the two aspects, we plan to study a conformally coupled scalar field model and an anisotropic inflation model. Firstly, we compare manifold corrections with symplectic integrators by numerical experiments, and discuss some chaotic indicators which are widely used in flat spacetime. Then, as for the most sensitive indicator, it will be used in curve spacetime after being corrected. At last, we will study deeply nonlinear behavior of the scalar field model, discuss dynamic and chaos caused by parameter's change. We hope our research will provide more theoretical interpretation for the accelerated expansion.

英文关键词： scalar field；chaos indicators；string；conservative systems；dissipative systems