$$\begin{aligned}
\left\{
\begin{array}{l}
{\psi}_{\mathrm {min}} \simeq \sqrt{\frac{4}{3}}\frac{{\mu}M}{{\sigma}}
    \hspace{5ex}{\mathrm {for}} \hspace{1ex}{\sigma}\gg \sqrt{{\mu}M},\\
{\psi}_{\mathrm {min}} \simeq 2\sqrt{{ \mu}M}
    \hspace{5ex}{\mathrm {for}} \hspace{1ex}{\sigma}\ll \sqrt{{\mu}M}.
\end{array}
\right.\end{aligned}$$ Since the gauge symmetry of the waterfall fields $\Psi$ and $\bar{\Psi}$ is already broken during inflation, no topological defects are formed in this model. When $\sigma$ is larger than $\sqrt{\mu M}$, the effective potential is given by $$V_H({ \sigma}) \simeq 
{\mu}^4\left[1-\frac{2}{27}\frac{{\mu}^2M^2}{{\sigma}^4}+\frac{{\sigma}^4}{8}\right].$$ The third term reflects the effect of the supergravity. Since the effective potential is dominated by the false vacuum energy ${ \mu}^4$, the Hubble parameter is given by $$H \simeq \frac{{ \mu}^2}{\sqrt{3}}.$$ To consider the dynamics of the inflation, we differentiate the effective potential as $$\frac{{\partial} V_H}{{\partial}{ \sigma}} =
{ \mu}^4\left[\frac{8}{27}\frac{({\mu}M)^2}{{ \sigma}^5}
 + \frac{1}{2}{ \sigma}^3\right].$$ The second term, which reflects the effect of the supergravity, dominates the inflation dynamics when inflaton $ \sigma$ is larger than $ {\sigma}_d$ given by $${ \sigma}_d = \left(\frac{16}{27}\right)^{1/8}\left({\mu}M\right)^{1/4}.$$ Let us define $\sigma_{i}$ as the value of the inflaton field when the pivot scale $k_0=0.002[{\mathrm {Mpc}}^{-1}]$ leaves the horizon. The slow-roll condition is broken when $|{ \eta}| = |\frac{1}{2}\frac{V''}{V}|\sim1$ and inflation ends at $ { \sigma} \simeq { \sigma}_c$ where $${ \sigma}_c = \left(\frac{40}{27}\right)^{1/6}\left({ \mu}M\right)^{1/3}.$$ Then, the number of $e$-folds $N_H$ from 