Enhancement of second-order gravitational waves at Q-ball decay

Abstract The recent observation of 4 He favors a large lepton asymmetry at the big bang nucleosynthesis. If Q-balls with charge decay after electroweak phase transition, such can be generated without producing too baryon asymmetry. In this scenario, dominate universe before and induces sharp transition from early matter-dominated era to radiation-dominated era. gravitational waves (GWs) are enhanced through second-order effect scalar perturbations. We evaluate density produced GWs show that pulsar timing array observations probe scenario depending on amplitude