论文标题
弗里德曼方程的无限尺寸对称组
Infinite dimensional symmetry groups of the Friedmann equations
论文作者
论文摘要
在存在宇宙恒定项的情况下，我们发现了从完美流体来源发出的弗里德曼方程的对称发生器。相关的动力学被认为由两个耦合的一阶普通微分方程，连续性和二次约束方程来控制。任意功能出现在对称矢量的组件中，表明该组的无穷大。当状态方程被认为是任意但从头开始时，先前已知的结果将被恢复和/或广义化。当在动态变量中考虑压力时，具有不同状态方程的模型的解决方案将彼此映射；因此，从简单的已知情况开始，将解决方案呈现给具有复杂状态方程的模型。
We find the symmetry generators for the Friedman equations emanating from a perfect fluid source, in the presence of a cosmological constant term. The relevant dynamics is seen to be governed by two coupled, first order ordinary differential equations, the continuity and the quadratic constraint equation. Arbitrary functions appear in the components of the symmetry vector, indicating the infinity of the group. When the equation of state is considered as arbitrary but ab initio given, previously known results are recovered and/or generalized. When the pressure is considered among the dynamical variables, solutions for models with different equations of state are mapped to each other; thus enabling the presentation of solutions to models with complicated equations of state starting from simple known cases.
