existence of the gravitational waves which is provided by the observation of the binary pulsar $1913+16$ [@Hulse:1974eb]. Yet up to date no direct detection has been made. In the world, there are lots of ongoing and planned experiments to detect the gravitational waves directly. Laser Interferometer Gravitational-Wave Observer (LIGO) [@LIGO] is working on the ground in USA. In Europe, Virgo [@Virgo] commenced operations in 2007 and Einstein Telescope (ET) [@ET] is planned. In Japan, KAGRA [@KAGRA] is now under construction. It is also planned to construct the space-borne interferometers such as Laser Interferometer Space Antenna (LISA) [@LISA],  Deci-hertz Interferometer Gravitational Wave Observatory (DECIGO)  [@DECIGO1; @Seto:2001qf; @Kawamura:2011zz], and Big Bang Observer (BBO) [@Crowder:2005nr].

The direct detection experiments of the gravitational waves are expected to provide rich information about various astrophysical phenomena, but one of the ultimate goals of the experiments is to probe the early history of the universe. It is presumed that in the very early universe the vacuum energy dominates the universe and causes quasi-exponential expansion of the universe called inflation. Inflation explains the homogeneity and flatness of the universe. Planck satellite [@Ade:2013zuv] has measured anisotropies of the cosmic microwave background (CMB) and successfully determined the cosmological parameters with 