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 } \gtrsim 10 ^ { -5 } \operatorname { 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 .