The organization of this paper is as follows. We review the double inflation model in Sec. \[sec:Smooth hybrid inflation\]. In Sec. \[sec:gw\_production\], we calculate the amount of the produced gravitational waves by using analytical consideration and lattice simulations. We estimate the present density of the gravitational waves and the peak frequency in Sec. \[sec:present\_density\]. Finally, Sec. \[sec:conclusion\] is devoted to the conclusion.

Smooth hybrid new inflation {#sec:Smooth hybrid inflation}
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In this section, we review the smooth hybrid new inflation model in supergravity proposed in [@Yamaguchi:2004tn]. This model has two inflationary stages. At first, the smooth hybrid inflation [@Lazarides:1995vr], whose gauge symmetry is already broken at the beginning of the inflation differently from the hybrid inflation model based on supergravity  [@Linde:1997sj], takes place. After the first inflationary stage, the new inflation [@Izawa:1996dv] follows. We assume that the $e$-fold number of the new inflation is smaller than $~60$. Thus, the density fluctuations on large scales are produced during the smooth hybrid inflation. In this section, we set the reduced planck mass $ M_{\mathrm{pl}} \simeq 2.4\times10^{18}{\mathrm{GeV}}$ equal to unity unless otherwise stated.

Smooth hybrid inflation
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First, we discuss the smooth hybrid inflation model. This model has three superfields. One is the 