Abstract
The propagation of weak gravitational waves on the background of dark energy is studied. The consideration is carried out within the framework of an approximate approach where the cosmological scale factor is expanded as a power series for relatively small values of the redshift corresponding to the epoch of the present accelerated expansion of the universe. For several different dark energy models, we obtain dispersion relations for gravitational waves which can be used to estimate the viability of every specific model by comparing with observational data.