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 cT of primordial gravitational waves may deviate from unity. We find that the steplike variation of cT 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 cT. Thus provided that the foreground contribution is under control, high-precision cosmic microwave background (CMB) polarization observations will be able to put tight constraint on the variation of cT, and so the corresponding theories.