this work, we show that the double inflation model, which was originally proposed in  [@Randall:1995dj; @GarciaBellido:1996qt; @Izawa:1997df] to solve the initial value problem for the new inflation, produces gravitational waves with the wavelength long enough to be proved with the planned detectors.

In the double inflation, there are two inflationary stages. In this paper, we consider the smooth hybrid new inflation model [@Yamaguchi:2004tn]. At the first stage, smooth hybrid inflation  [@Lazarides:1995vr; @Jeannerot:2000sv] occurs, followed by the second stage at which new inflation occurs. In the intermediate stage, the inflaton and waterfall fields oscillate around the minimum of the potential in the same way as the reheating. Since in the smooth hybrid inflation, the gauge symmetry of the waterfall fields is broken even during the inflation, no harmful topological defects are produced. In the previous study [@Kawasaki:2006zv], it was found that in this model fluctuations of the scalar fields are enhanced by the parametric resonance and then primordial black holes are formed at a characteristic scale. In this paper, we pay attention to the production of the gravitational waves from these fluctuations. Since the parametric resonance is a nonlinear phenomenon, we calculate the production of the gravitational waves with lattice simulations.

