The refractive index of the relic gravitons and the nHz band

TL;DR

This paper explores how a varying refractive index of relic gravitons during inflation can produce a blue-tilted spectrum detectable in the nHz range, potentially explaining pulsar timing array signals.

Contribution

It introduces a model linking the evolution of the refractive index during inflation to observable gravitational wave signatures in the nHz band, compatible with current bounds.

Findings

Refractive index increase leads to a blue spectral energy density.

Pulsar timing arrays can probe the refractive index evolution during inflation.

Model aligns with bounds from wide-band interferometers and pulsar data.

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 the 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.