Lensing bias on cosmological parameters from bright standard sirens

Abstract: Next generation gravitational waves (GWs) observatories are expected to measure GW signals with unprecedented sensitivity, opening new, independent avenues to learn about our Universe. The distance-redshift relation is a fulcrum for cosmology and can be tested with GWs emitted by merging binaries of compact objects, called standard sirens, thanks to the fact that they provide the absolute distance from the source. On the other hand, fluctuations of the intervening matter density field induce modifications on the measurement of luminosity distance compared to that of a homogeneous universe. Assuming that the redshift information is obtained through the detection of an electromagnetic counterpart, we investigate the impact that lensing of GWs might have in the inference of cosmological parameters. We treat lensing as a systematic error and check for residual bias on the values of the cosmological parameters. We do so by means of mock catalogues of bright sirens events in different scenarios relevant to Einstein Telescope. For our fiducial scenario, the lensing bias can be comparable to or greater than the expected statistical uncertainty of the cosmological parameters, although non-negligible fluctuations in the bias values are observed for different realisations of the mock catalogue. We also discuss some mitigation strategies that can be adopted in the data analysis. Overall, our work highlights the need to model lensing effects when using standard sirens as probes of the distance-redshift relation.