Propagating speed of primordial gravitational waves and inflation

We show that if the propagating speed of gravitational waves (GWs) gradually diminishes during inflation, the power spectrum of primordial GWs will be strongly blue, while that of the primordial scalar perturbation may be unaffected. We also illustrate that such a scenario is actually a disformal dual to the superinflation, but it does not have the ghost instability. The blue tilt obtained is $0<n_T\lesssim 1$, which may significantly boost the stochastic GW background at the frequency band of Advanced LIGO/Virgo, as well as the space-based detectors.