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

Understand

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.