标题： 非最小耦合常数和原始de Sitter态 显示英文标题

标题： The non-minimal coupling constant and the primordial de Sitter state

摘要： 采用动力系统方法研究了一个带有非最小耦合标量场和势函数的平坦Friedmann-Robertson-Walker宇宙学模型的动力学。所进行的分析区分了非最小耦合常数参数$\xi=\frac{3}{16}$的值，这是五维引力理论中的共形耦合。结果表明，对于标量场在无穷大处的单项式势函数，存在典型的de Sitter状态和Einstein-de Sitter状态。对于势函数不比线性更快变化的情况，de Sitter状态相对于宇宙膨胀是不稳定的。这导致了一种没有初始奇点的典型宇宙演化。 显示英文摘要

摘要： Dynamical systems methods are used to investigate dynamics of a flat Friedmann-Robertson-Walker cosmological model with the non-minimally coupled scalar field and a potential function. Performed analysis distinguishes the value of non-minimal coupling constant parameter $\xi=\frac{3}{16}$, which is the conformal coupling in five dimensional theory of gravity. It is shown that for a monomial potential functions at infinite values of the scalar field there exist generic de Sitter and Einstein-de Sitter states. The de Sitter state is unstable with respect to expansion of the Universe for potential functions which do not change faster than linearly. This leads to a generic cosmological evolution without the initial singularity.