We discuss propagation of the axial gravitational waves (AGWs) in the spatially flat conformal Friedmann–Lemaitre–Robertson–Walker (FLRW) spacetime, which is dominated by a perfect fluid, in the generalized Rastall theory of gravity (gRT). On this purpose, we perturb the spatially flat metric, background material content and the four-velocity components with the help of Regge–Wheeler perturbations inducing AGWs and formulate the corresponding field equations for both unperturbed and perturbed metrics. Then, we focus on these equations to discuss evolution of the perturbation parameters in the radiation as well as the dust, stiff-fluid and the dark energy dominated phases of the cosmos. We see that material distribution of the background geometry does not feel the propagation of axial modes and the AGWs can produce changes in the velocity components similar to the general relativity (GR) case. As a result, we conclude that the matter-curvature coupling changes the evolution of perturbation parameters and thus the propagation of AGWs and their amplitudes.

我们在广义的拉斯塔尔重力理论（gRT）中讨论轴向重力波（AGW）在空间平坦的共形Friedmann–Lemaitre–Robertson–Walker（FLRW）时空中的传播，该时空以理想流体为主。为此，我们借助Regge-Wheeler扰动诱导AGW扰动了空间平面度量，背景材料含量和四速度分量，并针对不受扰动和受扰动的度量公式制定了相应的场方程。然后，我们重点关注这些方程式，以讨论辐射中微扰参数的演变以及宇宙的尘埃，硬质流体和暗能量占主导的相。我们看到背景几何形状的材料分布没有感觉到轴向模态的传播，并且AGW可以产生类似于广义相对论（GR）情况的速度分量变化。结果，我们得出结论，物质-曲率耦合改变了扰动参数的演变，从而改变了AGW的传播及其幅度。