Enhanced curvature perturbations from spherical domain walls nucleated during inflation

Abstract

We investigate spherical domain walls~(DWs) nucleated via quantum tunneling in multifield inflationary models and curvature perturbations induced by the inhomogeneous distribution of those DWs. We consider the case that the Euclidean action $S_{E}$ of DWs changes with time during inflation so that most of DWs nucleate when $S_{E}$ reaches the minimum value and the radii of DWs are almost the same. When the Hubble horizon scale exceeds the DW radius after inflation, DWs begin to annihilate and release their energy into background radiation. Because of the random nature of the nucleation process, the statistics of DWs is of the Poisson type and the power spectrum of curvature perturbations has a characteristic slope ${\cal P}_{\cal R}(k)\propto k^{3}$. The amplitude of ${\cal P}_{\cal R}(k)$ depends on the tension and abundance of DWs at the annihilation time while the peak mode depends on the mean separation of DWs. We also numerically obtain the energy spectra of scalar-induced gravitational waves from predicted curvature perturbations which are expected to be observed in multiband gravitational-wave detectors.