[Paper Review] Flat Energy Spectrum of Primordial Gravitational Waves vs Peaks and the NANOGrav 2023 Observation

V. K. Oikonomou|arXiv (Cornell University)|Jun 30, 2023

Cosmology and Gravitation Theories5 citations

TL;DR

This paper proposes that the 2023 NANOGrav nHz stochastic gravitational wave signal can be explained by cosmological models featuring a blue-tilted primordial gravitational wave spectrum and an abnormal reheating era, with viable mechanisms including $f(R)$ gravity, Einstein-Gauss-Bonnet theory, and a Higgs-axion model with short slow-roll axion phases. A reheating temperature of $\mathcal{O}(400)$ GeV and a blue tensor spectral index are key to compatibility with observations.

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.

Motivation & Objective

• To identify viable cosmological models that can explain the 2023 NANOGrav observation of a stochastic gravitational wave background in the nHz band.
• To determine the conditions under which primordial gravitational wave energy spectra—flat or peak-like—can be compatible with the NANOGrav data.
• To investigate the role of reheating temperature and tensor spectral index in matching the observed signal's spectral slope.
• To evaluate whether modified gravity theories and axion-Higgs interactions can produce a detectable signal in NANOGrav and future experiments like LISA.
• To assess the cosmological origin of the NANOGrav signal against astrophysical alternatives using Bayesian model comparison.

Proposed method

• Analyzes $f(R)$ gravity models with geometrically induced abnormal reheating eras to generate a flat or peak-like primordial gravitational wave spectrum.
• Evaluates Einstein-Gauss-Bonnet gravity models that predict a positive tensor spectral index, leading to a blue-tilted spectrum.
• Examines a Higgs-axion model with higher-order non-renormalizable interactions that induce short slow-roll phases for the axion field post-electroweak symmetry breaking.
• Computes the primordial gravitational wave energy spectrum using the curvature perturbation and equation of state evolution during reheating.
• Applies constraints from Planck 2018 data and Bayesian model comparison to assess viability of proposed models.
• Compares predicted signal shapes across NANOGrav, LISA, and the Einstein Telescope to test detectability and distinguishability.

Experimental results

Research questions

• RQ1 Can modified gravity theories such as $f(R)$ gravity with abnormal reheating reproduce the NANOGrav 2023 signal's observed spectral slope?
• RQ2 What is the required tensor spectral index and reheating temperature for a primordial gravitational wave spectrum to match the NANOGrav observation?
• RQ3 Can a Higgs-axion model with transient slow-roll axion phases generate a detectable peak in the gravitational wave energy spectrum?
• RQ4 How do the predicted signal shapes in NANOGrav, LISA, and the Einstein Telescope differ across competing models?
• RQ5 Is the cosmological origin of the NANOGrav signal statistically favored over astrophysical explanations like supermassive black hole binaries?

Key findings

• A blue-tilted tensor spectral index combined with a reheating temperature of $\mathcal{O}(400)$ GeV is necessary to explain the NANOGrav 2023 signal in most models.
• The $f(R)$ gravity model with geometrically induced abnormal reheating can produce a flat or peak-like energy spectrum compatible with the NANOGrav observation.
• The Higgs-axion model with short slow-roll axion phases can generate a characteristic peak in the gravitational wave spectrum detectable by both NANOGrav and LISA, but not by the Einstein Telescope.
• Einstein-Gauss-Bonnet models with a significant blue-tilted tensor spectrum and low reheating temperature can also explain the signal, though such spectra are constrained by Planck 2018 data.
• The non-local version of the Starobinsky model is identified as a viable candidate due to its ability to produce a large blue-tilted spectral index while remaining consistent with cosmological constraints.
• Bayesian model comparison favors cosmological models over astrophysical ones by a factor of 10 to 100, supporting a cosmological origin for the signal.