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Recently, we have shown that the propagation speed $c_T$ of the primordialgravitational waves (GWs) might be nontrivially varying during inflation, whichcould induce local oscillations in the power spectrum of primordial GWs. Inthis paper, we numerically confirm that, although with a disformal redefinitionof the metric the nontrivial $c_T$ may be set as unity, the power spectrum inthe frame with $c_T=1$ is completely the same as that in the original disformalframe, 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 varyingHubble parameter. In addition, we also clarify how to obtain a blue-tilted GWsspectrum by imposing a rapidly decreasing $c_T$ during inflation.

Is there an effect of a nontrivial $c_T$ during inflation?