论文标题
关于$ r+αr^{2} $重力理论中简单宇宙学模型的结构稳定性
On the structural stability of a simple cosmological model in $R+αR^{2}$ theory of gravity
论文作者
论文摘要
使用动力学系统方法研究了标态曲率的二次贡献的重力理论。最简单的弗里德曼（Robertson-Robertson） - 采用了walker指标来制定约旦框架和共形的爱因斯坦框架中的动力学。我们表明，在这两个框架中，都有稳定的de de de de Sitter状态，其中哈勃函数的扩展自然包含与有效的暗物质成分相对应的术语。使用不变的中心歧管，我们证明，在爱因斯坦框架中，存在从不稳定到稳定的de de de de de de de的初始条件的零量度集合。另外，最初的DE Sitter状态与相反的传播奇点有关。我们表明，在约旦框架和爱因斯坦框架中，该理论的表述在物理上是不差异的。
The theory of gravity with a quadratic contribution of scalar curvature is investigated using a dynamical systems approach. The simplest Friedmann--Robertson--Walker metric is employed to formulate the dynamics in both the Jordan frame and the conformally transformed Einstein frame. We show that, in both frames, there are stable de Sitter states where the expansion of the Hubble function naturally includes terms corresponding to an effective dark matter component. Using the invariant center manifold, we demonstrate that, in the Einstein frame, there exists a zero-measure set of initial conditions that lead from an unstable to a stable de Sitter state. Additionally, the initial de Sitter state is associated with a parallelly propagated singularity. We show that the formulations of the theory in the Jordan frame and the Einstein frame are physically nonequivalent.
