Gravitational waves in the presence of viscosity

We analyze gravitational waves propagating in an isotropic cosmic fluid endowed with a bulk viscosity zeta and a shear viscosity eta, assuming these coefficients to vary with fluid density rho as rho(lambda), with lambda = 1/2 favored by experimental evidence. We give the general governing equation for the gravitational waves and focus thereafter on two examples. The first concerns waves in the very late universe, close to the Big Rip, where the fate of the cosmic fluid is dependent highly on the values of the parameters. Our second example considers the very early universe, the lepton era, the motivation for this choice being that the microscopical bulk viscosity as calculated from statistical mechanics is then at maximum. We find that the gravitational waves on such an underlying medium are damped, having a decay constant equal to the inverse of the conformal Hubble parameter. Our results turn out to be in good agreement with other viscosity-based approaches.