Lepton asymmetry in the primordial gravitational wave spectrum

Effects of neutrino free streaming is evaluated on the primordial spectrum of gravitational radiation taking both neutrino chemical potential and masses into account. The former or the lepton asymmetry induces two competitive effects, namely, to increase anisotropic pressure, which damps the gravitational wave more, and to delay the matter-radiation equality time, which reduces the damping. The latter effect is more prominent and a large lepton asymmetry would reduce the damping. We may thereby be able to measure the magnitude of lepton asymmetry from the primordial gravitational wave spectrum.