Nanohertz gravitational waves from domain walls nucleated during inflation

Abstract

We investigate scalar-induced gravitational waves (SIGWs) produced by domain walls (DWs) nucleated via quantum tunneling during inflation with an extended nucleation time. In contrast to the small-period nucleation framework, in which DWs form over a narrow interval and possess nearly identical radii, we show that an extended nucleation period leads to a distribution of DW radii characterized by $\gamma\equiv\overline{R^4}/(\overline{R^2})^2>1$, which enhances the resulting curvature perturbations. We construct a two-field inflation model with an inflaton $\phi$ and a spectator field $\chi$ coupled through the potential $V(\phi,\chi)$, where the DW tension $\sigma(t)$ evolves smoothly as the inflaton rolls past a critical value. The characteristic width of this transition determines the cutoff scale $k_{\text{cut}}$ of the curvature power spectrum, enabling the SIGW peak to be placed in the nanohertz frequency band with detectable amplitude. For three representative parameter sets, we compute the SIGW spectra and find that the peak frequency ranges from $\sim10^{-8}$\,Hz to $\sim10^{-2}$\,Hz, with the nanohertz-peaked spectrum matching the NANOGrav and EPTA signals for suitable parameter choices. By selecting different parameters, our model can produce signals detectable by different gravitational-wave detectors.