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, where DWs form instantaneously and produce a curvature power spectrum too weak to account for the nanohertz stochastic gravitational-wave background (SGWB) reported by pulsar timing array (PTA) collaborations, we show that a finite nucleation duration leads to a distribution of DW radii characterized by $γ\equiv\overline{R^4}/(\overline{R^2})^2>1$, which enhances the resulting curvature perturbations. We construct a two-field inflation model with an inflaton $ϕ$ and a spectator field $χ$ coupled through the potential $V(ϕ,χ)$, where the DW tension $σ(t)$ 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 nanohertz-peaked spectrum matching the NANOGrav and EPTA signals. By selecting different parameters, our model simultaneously predicts potentially observable signals at other gravitational-wave detectors.