Gravitational Wave From Axion-like Particle Inflation
  In this paper, we investigate the Axion-like Particle inflation by applying
the multi-nature inflation model, where the end of inflation is achieved
through the phase transition (PT). The events of PT should not be less than
$200$, which results in the free parameter $n\geq404$. Under the latest CMB
restrictions, we found that the inflation energy is fixed at $10^{15}
\rm{GeV}$. Then, we deeply discussed the corresponding stochastic background of
the primordial gravitational wave (GW) during inflation. We study the two kinds
of $n$ cases, i.e., $n=404, 2000$. We observe that the magnitude of $n$ is
negligible for the physical observations, such as $n_s$, $r$, $\Lambda$, and
$\Omega_{\rm{GW}}h^2$. In the low-frequency regions, the GW is dominated by the
quantum fluctuations, and this GW can be detected by Decigo at
$10^{-1}~\rm{Hz}$. However, GW generated by PT dominates the high-frequency
regions, which is expected to be detected by future 3DSR detector.
