Gravitational wave luminosity distance in viscous cosmological models

We study the so-called Gravitational Wave luminosity distance-redshift relation dGW L (z) during cosmological eras driven by non-perfect fluids. In particular, we show that the presence of a shear viscosity in the energy momentum tensor turns out to be the most relevant effect. Within this scenario, a constant shear viscosity imprints the gravitational wave propagation through a friction term (z) with a uniquely given redshift dependence. This peculiar evolution predicts a specific shape for the ratio dGW L /dEM L which tends to a constant value when the sources are at z & 1, whereas scales linearly with the shear viscosity at lower redshifts, regardless of the value of m0. According to our final discussion, the predicted redshift dependence (z) provided by a shear viscosity could be tested by upcoming surveys of multi-messenger sources against analogous scenarios provided by some widely studied theories of modified gravity.