high precision, which supports the prediction of the inflationary theories. However, it is impossible to prove directly the era before photons decouple from electrons, if we use the result of the observation of cosmic microwave background only. In order to study the early universe before photon decoupling, we use the gravitational wave since the gravitational wave interacts with other particles very weakly and preserves the information about the early universe.

In this paper, we discuss the gravitational wave production from inflation. There are several primordial origins of the gravitational waves: quantum fluctuations of the metric [@Lyth:2009zz], preheating  [@Khlebnikov:1997di; @Easther:2006gt; @GarciaBellido:2007af; @Dufaux:2008dn], domain walls [@Hiramatsu:2010yz; @Kawasaki:2011vv], cosmic strings  [@Berezinsky:2000vn; @Kawasaki:2010yi; @Damour:2000wa; @Damour:2004kw], and so on. In this paper, we focus on the preheating as the origin of gravitational waves. After the end of the inflation, the inflaton rapidly oscillates around the true vacuum, interacting with other scalar fields. At this epoch, fluctuations of the scalar fields enhanced vastly  [@GarciaBellido:1997wm; @Felder:2000hj], which produce abundant amount of gravitational waves. However, in general, the wavelength of the gravitational waves produced from reheating is so short [@Dufaux:2008dn] that we cannot detect the gravitational waves even in the future gravitational wave experiments with high sensitivity. In 