Propagation of gravitational waves in various cosmological backgrounds

The present work investigates some exact solutions of the gravitational wave equation in widely used cosmological spacetimes. examples are taken from spatially flat and closed isotropic models as well Kasner metric which is anisotropic. Various matter distributions considered, standard dust or radiation distribution to exotic matters like that with an state $$P = - \frac{1}{3} \rho $$ . In almost all cases frequency amplitude found be decaying evolution, except for a universe where there resurgence waveform, consistent recollapse into big crunch singularity.