标题： 广义贝肯斯坦理论Palatini形式中的线性化物理和引力波极化 显示英文标题

标题： Linearized physics and gravitational-waves polarizations in the Palatini formalism of GBD theory

摘要： 在Palatini形式框架下提出了一种广义Brans-Dicke（GBD）理论。 我们通过变分方法推导出场方程，并通过弱场近似方法得到线性化方程。 我们展示了GBD理论在Palatini形式中的几何标量场的各种性质：它是无质量且无源的，这与GBD理论在度规形式中的结果不同。 此外，我们通过测地线偏离方法和Newman-Penrose方法研究了Palatini-GBD理论中的引力波（GWs）的极化模式。 观察到在Palatini-GBD理论中存在三种极化模式和四种振荡。 具体来说，它们是两个横向张量（$+$）和（$\times$）标准极化模式，以及一个呼吸模式（具有两种振荡）。 Palatini-GBD理论中的引力波极化结果与度规-GBD理论中的结果不同，在度规-GBD理论中存在四种极化模式：两个标准张量模式（$+$和$\times$）、一个标量呼吸模式和一个质量型标量模式，该模式是纵向和呼吸极化的混合。 与Palatini-$f(\tilde{R})$理论和广义相对论相比，可以看出在Palatini-GBD理论中可以发现引力波极化的额外呼吸模式。 最后，推导出了参数化后牛顿（PPN）参数的表达式，该参数可以通过实验测试。 显示英文摘要

摘要： A generalized Brans-Dicke (GBD) theory in the framework of Palatini formalism are proposed in this paper. We derive the field equations by using the variational approach and obtain the linearized equations by using the weak-field approximation method. We show various properties of the geometrical scalar field in the Palatini-formalism of GBD theory: it is massless and source-free, which are different from the results given in the metric-formalism of GBD theory. Also, we investigate the polarization modes of gravitational waves (GWs) by using the the geodesic deviation method and the Newman-Penrose method in the Palatini-GBD theory. It is observed that there are three polarizations modes and four oscillation in the Palatini-GBD theory. Concretely, they are the two transverse tensor ($+$) and ($\times$) standard polarization modes, and one breathing mode (with two oscillation). The results of GWs polarization in the Palatini-GBD theory are different from that in the metric-GBD theory, where there are four polarizations modes: the two standard tensorial modes ($+$ and $\times$), a scalar breathing mode, and a massive scalar mode that is a mix of the longitudinal and the breathing polarization. Comparing with the Palatini-$f(\tilde{R})$ theory and the General Relativity, we can see that the extra breathing mode of GWs polarization can be found in the Palatini-GBD theory. At last, the expression of the parameterized post Newton (PPN) parameter is derived, which could pass through the experimental test.