Blue and violet graviton spectra from a dynamical refractive index

TL;DR

This paper explores how a dynamical refractive index during inflation can produce a relic graviton spectrum with distinctive features, potentially detectable in the kHz and mHz frequency ranges, consistent with current constraints.

Contribution

It introduces a model where a dynamical refractive index during inflation alters the relic graviton spectrum, highlighting new detectable features in the gravitational wave background.

Findings

Spectral energy distribution mildly increases at frequencies below μHz.

A high-frequency plateau appears between mHz and audio band.

Potentially detectable signals in the kHz and mHz regions.

Abstract

We show that the spectral energy distribution of relic gravitons mildly increases for frequencies smaller than the $\mu$Hz and then flattens out whenever the refractive index of the tensor modes is dynamical during a quasi-de Sitter stage of expansion. For a conventional thermal history the high-frequency plateau ranges between the mHz and the audio band but it is supplemented by a spike in the GHz region if a stiff post-inflationary phase precedes the standard radiation-dominated epoch. Even though the slope is blue at intermediate frequencies, it may become violet in the MHz window. For a variety of post-inflationary histories, including the conventional one, a dynamical index of refraction leads to a potentially detectable spectral energy density in the kHz and in the mHz regions while all the relevant phenomenological constraints are concurrently satisfied.