The refractive index of the relic gravitons and the nHz band

Massimo Giovannini

doi:10.1140/epjc/s10052-022-10050-4

Abstract

If the refractive index of the relic gravitons increases during a conventional stage of inflationary evolution the spectral energy density is blue at intermediate frequencies above the fHz and then flattens out after a knee that is typically smaller than the mHz. We investigate here the conditions leading to a sufficiently large spectral energy density in the nHz range where some peculiar signatures observed with the pulsar timing arrays have been recently attributed to cosmic gravitons. If these potential evidences are combined with the most recent bounds provided by wide-band interferometers in the audio range (i.e. between few Hz and the kHz) the allowed regions of the parameter space are compatible with both determinations and also with all the other constraints associated with the background of relic gravitons produced during inflation. The present analysis suggests that the pulsar timing arrays are sensitive to the evolution of the refractive index during early stages of the inflationary evolution. This physical interpretation of the preliminary empirical evidence is distinguishable from other perspectives since the high-frequency normalization, the blue spectral index and the tensor to scalar ratio cannot be independently assigned but are all related to the frequency of the knee that is ultimately determined by the competition between the rate of evolution of the refractive index and the slow-roll corrections.

Highlights

Gravitational waves acquire an effective index of refraction when they travel in curved space-times [6,7]. In this context the blue spectral slopes arise from a more mundane effect associated with the variation of the refractive index even if the background geometry evolves according to a conventional stage of expansion possibly supplemented by a standard decelerated epoch [8]
If parity breaking terms are included in the effective action [10,11], the relic graviton background may be polarized but this possibility has been already discussed elsewhere [12]
There are nongeneric models of inflation where the higher-order corrections assume a particular form since the inflaton has some particular symmetry or because the rate of inflaton roll remains constant, as it happens in certain fast-roll scenarios [13]

Summary

Introduction

Gravitational waves acquire an effective index of refraction when they travel in curved space-times [6,7]. The features of this purported signal would imply, in the present notations, that3 [27]: 10−8.6 < h20 gw(ν, τ0) < 10−9.8, 3 nHz < ν < 100 nHz. The Kagra, LIGO and Virgo collaborations, in their attempt to constrain the stochastic backgrounds of relic gravitons reported a limit [30] implying, in the case of a flat spectral energy density, gw(ν, τ0) < 5.8 × 10−9, 20

Results

Conclusion