Degenerate higher derivative theories beyond Horndeski: evading the Ostrogradski instability
Degenerate higher derivative theories beyond Horndeski: evading the Ostrogradski instability
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DOI：
10.1088/1475-7516/2016/02/034
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发表时间：
2015-10
影响因子：
6.4
通讯作者：
D. Langlois;K. Noui
中科院分区：
文献类型：
--
作者：
D. Langlois;K. Noui
具有高阶时间导数的理论通常会遭受幽灵般的不稳定性，称为奥斯特罗格拉茨基不稳定性。这种命运可以通过考虑“退化”拉格朗日函数来避免，因为它的动力学矩阵不能求逆，从而导致规范变量之间的约束和物理自由度的减少。在这项工作中，我们推导出一个系统的方式退化条件的标量张量理论，二次依赖于一个标量场的二阶导数。因此，我们得到了这类标量-张量理论中所有退化理论的分类。四次Horndeski拉格朗日量及其在Horndeski之外的扩展属于这些退化情况。我们还确定了新的家庭标量张量理论的性质，他们是退化的，尽管他们的拉格朗日纯标量部分的非退化。
Theories with higher order time derivatives generically suffer from ghost-like instabilities, known as Ostrogradski instabilities. This fate can be avoided by considering ``degenerate'' Lagrangians, whose kinetic matrix cannot be inverted, thus leading to constraints between canonical variables and a reduced number of physical degrees of freedom. In this work, we derive in a systematic way the degeneracy conditions for scalar-tensor theories that depend quadratically on second order derivatives of a scalar field. We thus obtain a classification of all degenerate theories within this class of scalar-tensor theories. The quartic Horndeski Lagrangian and its extension beyond Horndeski belong to these degenerate cases. We also identify new families of scalar-tensor theories with the property that they are degenerate despite the nondegeneracy of the purely scalar part of their Lagrangian.