We consider the propagation of gravitational waves in the late-time Universe,
in the presence of structure, and we also consider the cosmic fluid to be
viscous. In this work, we investigate the cumulative effect of inhomogeneities
and viscosity of the cosmic-fluid, on the observables associated with the
sources of the gravitational waves. Employing Buchert’s averaging procedure in
the backreaction framework, we consider a model of inhomogeneous spacetime.
Using the modified redshift versus distance relation, through the averaging
process in the context of the model, we study the variation of the
redshift-dependent part of the observed gravitational wave amplitude for
different combinations of our model parameters, while simultaneously
considering damping of the gravitational wave amplitude due to viscosity of the
cosmic-fluid. Then, we investigate the differences occurring in the variation
of the redshift-dependent part of the observed gravitational wave amplitude,
due to consideration of viscous attenuation. We show that there are significant
deviations after the inclusion of viscous attenuation in our analysis,
depending on the chosen value of the coefficient of viscosity. Our result
signifies the importance of the effect of viscosity, within the model of an
inhomogeneous Universe, on precision measurements of parameters of
compact-binary sources of gravitational waves.
