In modified gravity theories, gravitational waves can propagate differently from general relativity and their propagating speed can be either constant or acquire a time dependence. We consider the constant models first and update the constraints on cosmological parameters from the combinations of $\mathrm{\text{Planck}}18+\mathrm{\text{BK}}18$ datasets. In this case, excluding superluminal propagation, we obtain the lower limit on the speed $c_g>0.22$ at 95% C.L. A non-trivial propagating speed impacts the amplitude of tensor spectrum by adding a factor $c_g^{n_t-1}$, where $n_t$ is the tensor tilt. We find that the value of $c_g$ has positive correlation with the tensor-to-scalar ratio and anti-correlation with the factor $c_g^{n_t-1}$. Then we explore a time-dependent speed which contains the resonance of the stochastic gravitational wave background. If the speed of gravitational waves oscillates at primordial era, resonance continuously enhances stochastic gravitational wave background which produces observable effects on tensor power spectra. We derive the constraints on the amplitude of oscillatory speed and tensor parameters from the combinations of $\mathrm{\text{Planck18}}+\mathrm{\text{BK18}}$ datasets. The numerical results show that the speed resonance of the stochastic gravitational wave background is sensitive to CMB observations.

在修正的引力理论中，引力波的传播方式与广义相对论不同，它们的传播速度可以是恒定的，也可以是与时间相关的。我们首先考虑常数模型，并根据以下组合更新宇宙学参数的约束$\mathrm{\text{普朗克}}18+\mathrm{\text{巴克}}18$数据集。在这种情况下，排除超光速传播，我们得到速度的下限$C_G>0。22$在 95% CL 时，重要的传播速度通过添加一个因子来影响张量谱的幅度$C_G^{n_t-1}$， 在哪里$n_t$是张量倾斜。我们发现，值$C_G$与张标量比呈正相关，与因子呈反相关$C_G^{n_t-1}$。然后我们探索包含随机引力波背景共振的时间相关速度。如果引力波的速度在太初时代振荡，共振会不断增强随机引力波背景，从而对张量功率谱产生可观察到的影响。我们从以下组合中得出对振荡速度幅度和张量参数的约束$\mathrm{\text{普朗克18}}+\mathrm{\text{BK18}}$数据集。数值结果表明，随机引力波背景的速度共振对CMB观测敏感。