Oscillating modulation to B-mode polarization from varying propagating speed of primordial gravitational waves

In low-energy effective string theory and modified gravity theories, the propagating speed $c_T$ of primordial gravitational waves may deviate from unity. We find that the step-like variation of $c_T$ during slow-roll inflation may result in an oscillating modulation to the B-mode polarization spectrum, which can hardly be imitated by adjusting other cosmological parameters, and the intensity of the modulation is determined by the dynamics of $c_T$. Thus provided that the foreground contribution is under control, high-precision CMB polarization observations will be able to put tight constraint on the variation of $c_T$, and so the corresponding theories.