QCD axion and gravitational waves in light of NANOGrav results

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 non-standard cosmological model driven by an exotic field $\phi$, in which the axion field provides the dark matter observed. For an equation of state $w_\phi < 1/3$, 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 by a QCD axion field evolving in a curvature-dominated background.