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QCD axion and gravitational waves in light of NANOGrav results

Nicklas Ramberg, Luca Visinelli · 2021 · 33 citationsRead the paper

The North American Nanohertz Observatory for Gravitational Waves (NANOGrav) collaboration has recently reported strong evidence for a stochastic process affecting the 12.5 yr dataset of pulsar timing residuals. We show that the signal can be interpreted in terms of a stochastic gravitational wave background emitted from a network of axionic strings in the early Universe. The spontaneous breaking of the Peccei-Quinn symmetry originate the axionic string network and the QCD axion, the dark matter particle in the model. We explore a nonstandard cosmological model driven by an exotic scalar field $\ensuremath{\phi}$ which evolves under the influence of a self-interacting potential; the axion field starts to oscillate during the modified cosmology, and provides the dark matter observed. For an equation of state ${w}_{\ensuremath{\phi}}<1/3$, the QCD axion mass is smaller than expected in the standard cosmology and the GW spectrum from axionic strings is larger. We assess the parameter space of the model which is consistent with the NANOGrav-12.5 yr detection, which can be explained within 95% limit by a QCD axion field evolving in a dust-like scenario, as well as within 68% limit in a cosmology with ${w}_{\ensuremath{\phi}}<0$.

What the full text shows

Theory or simulation

The NANOGrav-12.5 yr signal can be explained within 95% limit by a QCD axion field in a dust-like scenario (wφ ≈ 0) with a transition temperature Tφ < 10 MeV. — log10 A* ∈ (-14.9, -14.4), γ ~ 4.3 (wφ ≈ 0, Tφ < 10 MeV)
The NANOGrav-12.5 yr signal can be explained within 68% limit in a cosmology with wφ < 0. — log10 A* ∈ (-15.3, -14.6), γ ≈ (4.7 - 4.8) (wφ < -0.2, Tφ < 100 MeV)
Non-standard cosmology (NSC) with wφ < 1/3 results in a smaller QCD axion mass and a larger GW spectrum compared to standard cosmology. (wφ < 1/3)

Setup: Theoretical model based on NANOGrav-12.5 yr pulsar timing residuals (45 pulsars) and the Peccei-Quinn symmetry breaking mechanism.
How: The authors numerically solved coupled kinetic equations for an exotic scalar field φ and the QCD axion field's equation of motion to determine the Hubble rate and axion oscillations. They calculated the stochastic gravitational wave background (SGWB) emitted by a network of axionic strings evolving in this non-standard cosmology.
Limitations: The underlying model for the exotic component driving the NSC is not fully specified beyond the self-interacting potential. · GW emission is treated as a subdominant energy release mechanism compared to axion emission.

Summarized by Gemma 4 from the open-access full text · 8 Oct 2026. Read it