Relic gravitons at intermediate frequencies and the expansion history of the Universe

TL;DR

This paper investigates how different early Universe expansion scenarios affect relic graviton spectra, aiming to reconcile observational limits and potential signals across a wide frequency range.

Contribution

It introduces models of early Universe expansion with multiple stages and varying refractive index effects, analyzing their impact on relic graviton spectra and observational compatibility.

Findings

Spectral energy density undershoots pulsar timing signals at intermediate frequencies.

A secondary low-scale inflation can produce a local maximum in the graviton spectrum.

Increasing the refractive index during inflation results in a blue-tilted spectrum above the fHz, compatible with current observations.

Abstract

The early expansion history of the Universe is constrained by combining the most recent limits on the cosmic gravitons in the audio band and the claimed evidences of the nHz domain. The simplest scenario stipulates that between the end of inflation and the formation of light nuclei the evolution consists of a single phase expanding at a rate that is either faster or slower than the one of radiation. If there are instead multiple post-inflationary stages evolving at different rates, the spectral energy density always undershoots the signals potentially attributed to relic gravitons by the pulsar timing arrays at intermediate frequencies but ultimately develops a local maximum. After examining further complementary possibilities (like the presence of a secondary stage of inflation at low-scales) we analyze the early modifications of the effective expansion rate and argue that if the refractive index of the relic gravitons increases during a conventional inflationary epoch the spectral energy density is blue above the fHz and then flattens out in the $\mu$Hz region. In this instance the signal is compatible with the unconfirmed nHz observations, with the most recent limits of the wide-band interferometers and with the further constraints customarily imposed on the backgrounds of relic gravitons produced during inflation.