Recently , we have shown that the propagation speed c _ { T } of the primordial gravitational waves ( GWs ) might be nontrivially varying during inflation , which could induce local oscillations in the power spectrum of primordial GWs .
In this paper , we numerically confirm that , although with a disformal redefinition of the metric the nontrivial c _ { T } may be set as unity , the power spectrum in the frame with c _ { T } = 1 is completely the same as that in the original disformal frame , i.e. , the oscillating shape in the power spectrum is still reserved , since here the effect of c _ { T } is actually encoded in the nontrivially varying Hubble parameter .
In addition , we also clarify how to obtain a blue-tilted GWs spectrum by imposing a rapidly decreasing c _ { T } during inflation .