Phase transition during inflation and the gravitational wave signal at pulsar timing arrays

Gravitational wave signal offers a promising window into the dynamics of the early universe. The recent results from pulsar timing arrays (PTAs) could be the first glimpse of such new physics. In particular, they could point to new details during the inflation, which can not be probed by other means. We explore the possibility that the new results could come from the secondary gravitational wave sourced by curvature perturbations, generated by a first-order phase transition during the inflation. Based on the results of a field-theoretic lattice simulation of the phase transition process, we show that the gravitational wave signal generated through this mechanism can account for the new results from the PTAs. We analyze the spectral shape of the signal in detail. Future observations can use such information to distinguish the gravitational wave signal considered here from other possible sources.