that the new inflation occurs after the hybrid inflation, $N_{\mathrm{new}}$ should be larger than $0$. In addition to these conditions, the cut-off scale $M$ must be larger than $\mu$. These conditions are summarized as $$\begin{aligned}
\label{eq:condition}
\left\{
\begin{array}{ll}
(\mathrm{i}) &
  \sigma_{c}<\sigma_{i}<1\\[0.5\intextsep]
(\mathrm{i}\hspace{-.1em}\mathrm{i}) &
  \mu < 1\\[0.5\intextsep]
(\mathrm{i}\hspace{-.1em}\mathrm{i}\hspace{-.1em}\mathrm{i}) &
  \mu < M
  \\[0.5\intextsep]
(\mathrm{i}\hspace{-.1em}\mathrm{v}) &
  N_{\mathrm{H}}>10
  ,~
  N_{\mathrm{new}}>0
\end{array}
\right.\end{aligned}$$ Substituting (\[eq:mu\])$-$(\[eq:Nn\]) into (\[eq:condition\]), we can obtain the maximum and the minimum values of $\sigma_{i}$.

[c c]{}\

[c c]{}\

Fig. \[fig:simami\] shows the maximum and the minimum values of $\sigma_{i}$ at each value of $n_s$. Using (\[eq:mu\]) and (\[eq:M\]), we can get the corresponding maximum and the minimum values of $\mu$ and $M$ which are shown in Fig. \[fig:muM\].

Production of the gravitational waves {#sec:gw_production}
=====================================

During the oscillatory phase, the fluctuations of the scalar fields grow exponentially through the parametric resonance. These growing fluctuations can be a source for gravitational waves. In this section, we calculate the amount of the produced gravitational waves. First, we roughly calculate the energy density of the gravitational waves. Second, we introduce the formalism with which we calculate the energy density and the spectrum of the gravitational waves produced from the scalar fields. Finally, we 