无鬼类准伸缩子大引力中的矢量微扰
Vector Perturbations in Ghost-Free Quasidilaton Massive Gravity
AI总结：
研究无鬼准伸缩子大引力中最小物质对矢量微扰的影响，发现普通最小物质无法让分支II的矢量 sector 在线性微扰下保持健康，需选用分支I。
AI中文摘要：
我们研究了无鬼扩展准伸缩子大引力中无准伸缩子动能项且存在最小物质时的横向矢量微扰。在真空中，我们得到已知结果：在自加速分支J=0上，引力矢量模的动能系数K_V为零，因此这些模在线性阶无限强耦合。随后我们加入正则标量场和单个阿贝尔矢量（麦克斯韦场或普罗卡场），在积分掉辅助平移后，得到与真空中相同的K_V。标量物质没有横向微扰，它会进入未简化的平移约束，但一旦使用弗里德曼方程，这些项会抵消。具有各向同性背景为零的麦克斯韦场或普罗卡场，在二次阶不会与引力矢量混合。因此最小物质使分支II上的K_V保持为0。我们不声称这些模在非线性理论中不存在，仅得出结论：普通最小物质不足以使该分支上的矢量 sector 在微扰意义下保持健康。若需要线性阶下健康的引力矢量模，应使用分支I。
英文摘要：
We study transverse vector perturbations in ghost-free extended quasidilaton massive gravity without a quasidilaton kinetic term, in the presence of minimal matter. In vacuum, we recover the known result that the kinetic coefficient $K_V$ of the gravitational vector modes vanishes on the self-accelerating branch $J=0$, so those modes are infinitely strongly coupled at linear order. We then add a canonical scalar field and a single Abelian vector (Maxwell or Proca). After integrating out the auxiliary shift, we find the same $K_V$ as in vacuum. The scalar matter has no transverse perturbation; it enters the unsimplified shift constraint, but those terms cancel once the Friedmann equation is used. A Maxwell or Proca field with vanishing isotropic background does not mix with the gravitational vectors at quadratic order. Minimal matter therefore leaves $K_V=0$ on Branch II. We do not claim that the modes are absent from the nonlinear theory. We do conclude that ordinary minimal matter is not enough to make the vector sector perturbatively healthy on this branch. If we need healthy gravitational vector modes at the linear level, Branch I is the branch to use.
