Probing Primordial Black Hole Formation from Domain Wall Isocurvature Perturbations: Constraints and Implications

Domain walls are topological defects produced by the spontaneous symmetry-breaking of discrete symmetry during cosmological phase transitions. Domain walls can significantly contribute to the energy density in the late-evolution stage. We propose that the density perturbations from the fluctuations in the number density of the domain walls could collapse to form primordial black holes. This mechanism becomes effective when the domain wall energy density ratio to that of the radiation reaches about 0.1 in the radiation-dominated Universe. We find that models with $Z_2$ symmetry are excluded for interpreting pulsar timing array observations on the nano-Hz gravitational wave background since this model's domain wall number density fluctuations could lead to an overabundance of the primordial black holes. Moreover, the models, which generate approximately $N\sim 10$ domain walls from the spontaneous breaking of a discrete $Z_N$ symmetry, are also subject to stringent constraints due to the overproduction of primordial black holes.