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

TL;DR

This paper investigates the effects of a varying propagation speed of primordial gravitational waves during inflation, demonstrating that oscillations in the power spectrum persist even after disformal transformations and exploring conditions for a blue-tilted GW spectrum.

Contribution

It shows that the oscillating features in the GW power spectrum remain invariant under disformal transformations and explains how to generate a blue-tilted GW spectrum by decreasing $c_T$ rapidly.

Findings

Oscillations in the power spectrum are preserved under disformal redefinition.

The effect of $c_T$ is encoded in the varying Hubble parameter.

A rapidly decreasing $c_T$ can produce a blue-tilted GW spectrum.

Abstract

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.