In this talk, I present a bubble filtering-out mechanism for an asymmetric dark matter scenario during the Peccei-Quinn (PQ) phase transition. Based on a QCD axion model, extended by extra chiral neutrinos, I show that the PQ phase transition can be first order in the parameter space of the model and regarding the PQ symmetry breaking scale, the mechanism can generate PeV-scale heavy neutrinos as a dark matter candidate. Considering a CP-violating source, during the phase transition, discriminating between the neutrino and antineutrino number density, the observed dark matter relic abundance is found. I then obtain effective couplings of the QCD axion addressing the strong CP problem within the model. I also discuss about the energy density spectrum of gravitational waves generated from the first order phase transition and show that the signals can be detected by future ground-based detectors such as Einstein Telescope. In particular, for a visible heavy axion case of the model, it is shown that gravitational waves can be probed by DECIGO and BBO interferometers. Finally, I discuss the dark matter-standard model neutrino annihilation process as a source for the creation of PeV-scale neutrinos.
