Weak lensing of bright standard sirens: prospects for σ8

ABSTRACT Gravitational wave events with electromagnetic counterparts provide direct measurements of the Hubble diagram. We demonstrate that incorporating weak lensing into bright standard siren analyses allows measurements of cosmological parameters that do not influence the mean luminosity distance–redshift relation but do impact the cosmic structures. In particular, we examine the prospects for measuring the standard deviation of matter perturbations $\sigma _8$, in addition to the Hubble constant and the matter abundance. We find that a 10 per cent measurement of $\sigma _8$ would be feasible with the Einstein Telescope, provided a population of 300 neutron star binaries with electromagnetic counterparts is observed. With the Laser Interferometer Space Antenna, the measurement of $\sigma _8$ would have 30 per cent accuracy, assuming a population of 12 massive black hole binaries with electromagnetic counterparts is observed.