Looking at the NANOGrav signal through the anthropic window of axionlike particles

We explore the inflationary dynamics leading to formation of closed domain walls in course of evolution of an axion like particle (ALP) field whose Peccei-Quinn-like phase transition occurred well before inflationary epoch. Evolving after inflation, the domain walls may leave their imprint in stochastic gravitational waves background, in the frequency range accessible for the pulsar timing array measurements. We derive the characteristic strain power spectrum produced by the distribution of the closed domain walls and relate it with the recently reported NANOGrav signal excess. We found that the slope of the frequency dependence of the characteristic strain spectrum generated by the domain walls is very well centered inside the range of the slopes in the signal reported by the NANOGrav. Analyzing the inflationary dynamic of the ALP field, in consistency with the isocurvature constraint, we reveal those combinations of the parameters where the signal from the inflationary induced ALPs domain walls could saturate the amplitude of the NANOGrav excess. The evolution of big enough closed domain walls may end up in wormholes with the walls escaping into baby universes. We study the conditions when closed walls escape into baby universes and could leave a detectable imprint in the stochastic gravitational waves background.