FLRW 宇宙中的四次 Horndeski-Cartan 理论
Quartic Horndeski-Cartan theories in a FLRW universe
AI总结：
该研究在 FLRW 背景下考察四次 Horndeski-Cartan 理论，发现挠率不引入新自由度，仅修改传播，且族中仅一个理论的标量模式具有规则色散关系。
摘要：
我们在二阶形式主义下，考虑了具有挠率的四次 Horndeski 理论在 FLRW 背景上的情况。我们表明，存在一个单参数族的四次 Horndeski-Cartan 拉格朗日量，且所有这些理论仅修改了标准 Horndeski 理论在无挠时空上通常发现的引力子和标量扰动的色散关系。换句话说，对于此类理论，挠率不会引入新的自由度，而只会修改传播方式。尽管作用量中 Horndeski 标量与挠率场之间存在动力学混合，但这对一阶扰动成立。我们还表明，在四次 Horndeski-Cartan 理论族中，大多数拉格朗日量的标量模式的色散关系被彻底修改。我们仅发现该族中一个理论的标量模式具有规则的类波色散关系。
英文摘要：
We consider the Quartic Horndeski theory with torsion on a FLRW background in the second order formalism. We show that there is a one parameter family of Quartic Horndeski Cartan Lagrangians and all such theories only modify the dispersion relations of the graviton and the scalar perturbation that are usually found in the standard Horndeski theory on a torsionless spacetime. In other words, for the theories in this class torsion does not induce new degrees of freedom but it only modifies the propagation. This holds for first order perturbations in spite of a kinetic mixing between the Horndeski scalar with the torsion field in the action. We also show that for most Lagrangians within the family of Quartic Horndeski Cartan theories the dispersion relation of the scalar mode is radically modified. We find only one theory within the family whose scalar mode has a regular wave-like dispersion relation.
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