In light of the promising and imminent multi-messenger observational era, we suggest a method to constrain the cosmological background by future observation involving gravitational lensing of radiation emitted by a gravitational wave source.
We measure the impact of different cosmological parameters in the value of the time delay due to gravitational lensing. The measured time delay is between the gravitational radiation (in the wave optics regime) and the electromagnetic counterpart (in the geometrical optics approximation). Through this method we constrained the precision of the cosmological parameters involved. The results are promising and will give a considerable contribution in clarifying the Hubble tension problem.