  In this paper, we propose 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, we 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, we find the observed dark matter relic abundance, such that the
setup can be applied to the first order phase transition with different
strengths. We then calculate effective couplings of the QCD axion addressing
the strong CP problem within the model. We also study 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. Furthermore, we discuss the dark matter-standard model
neutrino annihilation process as a source for the creation of PeV-scale
neutrinos.

High Energy Physics - Phenomenology;Cosmology and Nongalactic Astrophysics