The propagating speed of relic gravitational waves and their refractive index during inflation

TL;DR

This paper investigates how a varying refractive index during inflation affects relic gravitational wave spectra, showing potential for detection with current and future gravitational wave observatories.

Contribution

It establishes a unified framework relating different parametrizations of the refractive index effect on gravitational waves during inflation.

Findings

Refractive index increase tilts the spectrum towards high frequencies.

Detectability of the gravitational waves is feasible with planned detectors.

Non-monotonic spectra with a maximum in the MHz range are possible.

Abstract

If the refractive index of the tensor modes increases during a conventional inflationary stage of expansion the relic graviton spectrum is tilted towards high frequencies. Two apparently diverse parametrizations of this effect are shown to be related by a rescaling of the four-dimensional metric through a conformal factor that involves the refractive index itself. Non-monotonic spectra with a maximum in the MHz region correspond to a limited variation of the refractive index terminating well before the end of inflation. After exploring a general approach encompassing the ones proposed so far, we estimate the required sensitivity for the direct detection of the predicted gravitational radiation and demonstrate that the allowed regions of the parameter space are within reach for some of the planned detectors operating either in the audio band (like Ligo/Virgo and Kagra) or in the mHz band (like Lisa, Bbo and Decigo).