Neutrino masses and gravitational wave background

We consider the Standard Model with three right-handed neutrinos to generate tiny neutrino masses by the seesaw mechanism. Especially, we investigate the case when one right-handed neutrino has the suppressed Yukawa coupling constants. Such a particle has a long lifetime and can produce an additional entropy by the decay. It is then discussed the impact of the entropy production on the gravitational wave background originated in the primordial inflation. We show that the mass and the coupling constants of the long-lived right-handed neutrino can be probed by the distortion of the gravitational wave spectrum, leading to the information of the mass of the lightest active neutrino.