On the interaction between thermalized neutrinos and cosmological gravitational waves above the electroweak unification scale

We investigate the interaction between the cosmological relic neutrinos, and primordial gravitational waves entering the horizon before the electroweak phase transition, corresponding to observable frequencies today nu_0 <= 10^-5 Hz. We give an analytic formula for the traceless transverse part of the anisotropic stress tensor, due to weakly interacting neutrinos, and derive an integro-differential equation describing the propagation of cosmological gravitational waves at these conditions. We find that this leads to a decrease of the wave intensity in the frequency region accessible to the LISA space interferometer, that is at the present the most promising way to obtain a direct detection of a cosmological gravitational wave. The absorbed intensity does not depend neither on the perturbation wavelength, nor on the details of neutrino interactions, and is affected only by the neutrino fraction f_nu. The transmitted intensity amounts to 88% for the standard value f_nu=0.40523. An approximate formula for non-standard values of f_nu is given.