论文标题
关于爱因斯坦 - 希尔伯特动作的非正式转变
On the Disformal Transformation of the Einstein-Hilbert Action
论文作者
论文摘要
非正式转化是对重力（相对性）和现代宇宙学主流研究生文本中通常阐述的众所周知的保形转换的概括。这种转换是标量张量理论中最重要的数学操作之一，试图解决涉及暗能量和暗物质的压迫问题。由于这个话题尚未渗透到这些文本，我们提出了爱因斯坦 - 希尔伯特动作的非正式转化的教学方向推导。在计算过程中，我们遇到了显然有问题的术语，这些术语可以解释为导致运动方程，而运动方程超出了衍生物的二阶，信号不稳定性。我们证明，可以通过Riemann曲率张量的定义来消除和吸收这些术语。转变的爱因斯坦 - 希尔伯特（Einstein-Hilbert）的作用被证明是霍恩德斯基（Horndeski）作用的特殊情况，其描述的标量场的运动方程仅在衍生物中只能达到二阶，这意味着稳定性。
Disformal transformation is a generalisation of the well-known conformal transformation commonly elaborated in mainstream graduate texts in gravity (relativity) and modern cosmology. This transformation is one of the most important mathematical operations in scalar tensor theories attempting to address pressing problems involving dark energy and dark matter. With this topic yet to penetrate these texts, we present a pedagogically oriented derivation of the disformal transformation of the Einstein-Hilbert action. Along the way of calculation, we encounter apparently problematic terms that could be construed as leading to equations of motion that go beyond second order in derivatives, signalling instability. We demonstrate that these terms can be eliminated and absorbed through the definition of the Riemann curvature tensor. The transformed Einstein-Hilbert action turns out to be a special case of the Horndeski action and the equations of motion for the scalar field that it describes are all up to second order only in derivatives, implying stability.
