发表机构
National Institute of Technology, Toyama College（富山工业高等专门学校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究在Weyl几何中构造了标量曲率任意函数的引力理论，证明其无鬼无快子条件等价于补偿标量动力学系数为正，并指出含常数、线性和二次项时必有有质量矢量和标量曲率子。
AI 中文摘要
Weyl几何允许在时空的每一点独立选择长度尺度，通过Weyl不变性（即局域尺度对称性）为推广广义相对论提供了自然框架。我们构造了一个引力理论，其拉格朗日量是Weyl几何中标量曲率的任意函数，并建立了该理论在最大对称真空附近无鬼和无快子的条件。对于任意函数，Weyl不变性要求除了度规和Weyl矢量之外，还存在一个补偿标量场。通过引入辅助场对作用量进行线性化，我们证明Weyl矢量仅通过标量场的一个单一组合与标量部分耦合。因此，Weyl矢量（平移该组合的对数梯度后）无需固定规范即成为Weyl不变的有质量矢量场。在爱因斯坦框架中，鉴于引力子无鬼，Weyl矢量的无快子条件与标量曲率子（与高曲率项相关的标量模式）的无鬼条件共同归结为补偿标量的动力学系数为正。当该系数为零时，标量曲率子不传播，仅留下引力子和有质量矢量。作为例子，我们表明对于包含常数、线性和二次曲率项的拉格朗日量，在整个稳定性区域内必然同时存在有质量矢量和有质量标量曲率子，而若没有线性项，标量曲率子则变为无质量。
英文摘要
Weyl geometry, in which the length scale can be chosen independently at each point of spacetime, provides a natural framework for extending general relativity through Weyl invariance, that is, local scale symmetry. We construct a gravitational theory whose Lagrangian is an arbitrary function of the scalar curvature in Weyl geometry and establish the conditions under which the theory is free of ghosts and tachyons around maximally symmetric vacua. For an arbitrary function, Weyl invariance requires a compensating scalar field in addition to the metric and the Weyl vector. By linearizing the action with an auxiliary field, we show that the Weyl vector couples to the scalar sector only through a single combination of the scalar fields. Consequently, the Weyl vector, shifted by the logarithmic gradient of this combination, becomes a Weyl-invariant massive vector field without gauge fixing. In the Einstein frame, given that the graviton is ghost-free, the no-tachyon condition for the Weyl vector, together with the no-ghost condition for the scalaron, the scalar mode associated with the higher-curvature terms, reduces to the positivity of the kinetic coefficient of the compensating scalar. When this coefficient vanishes, the scalaron does not propagate, leaving only the graviton and the massive vector. As an example, we show that for a Lagrangian containing constant, linear, and quadratic curvature terms, both a massive vector and a massive scalaron are necessarily present throughout the stability region, whereas without the linear term the scalaron becomes massless.
