Flat Energy Spectrum of Primordial Gravitational Waves vs Peaks and the NANOGrav 2023 Observation

TL;DR

This paper explores theoretical models predicting a flat or peaked primordial gravitational wave spectrum compatible with NANOGrav 2023 observations, emphasizing the role of blue tilt and reheating temperature in matching the data.

Contribution

It identifies specific conditions and models, including a Higgs-axion scenario, that can produce observable gravitational wave spectra consistent with recent detections.

Findings

A blue tilted spectrum with low reheating temperature can match NANOGrav data.

A Higgs-axion model predicts a detectable peak in gravitational waves for NANOGrav and LISA.

Certain models do not produce signals detectable by Einstein Telescope.

Abstract

In this work we present several characteristic examples of theories of gravity and particle physics scenarios that may yield an observable energy spectrum of stochastic primordial gravitational waves, compatible with the 2023 NANOGrav observations. The resulting theories yield a flat or a peak-like energy spectrum, and we further seek the conditions which if hold true, the energy spectrum can be compatible with the recent NANOGrav stochastic gravitational wave detection. As we show, in most cases a blue tilted spectrum combined with a relatively low reheating temperature is needed, the scale of which is determined by whether the radiation domination era is ordinary or it is an abnormal radiation domination era. One intriguing Higgs-axion model, which predicts short slow-roll eras for the axion field at the post-electroweak breaking epoch, which eventually change the total equation of state parameter at the reheating era, can explain the NANOGrav signal, if a blue tilted tensor spectral index inflationary era precedes the reheating era, and a reheating temperature of the order $\mathcal{O}(400)\,$GeV. This specific model produces an energy spectrum of primordial gravitational waves with a characteristic peak that is detectable from both the NANOGrav and future LISA experiment, but not from the future Einstein telescope.