Weak lensing of bright standard sirens: prospects for $\sigma_8$

TL;DR

This paper explores how weak lensing effects on bright standard sirens from gravitational waves can enable measurements of cosmological parameters like 88, independent of the mean luminosity distance, using future observatories.

Contribution

It introduces a novel method to measure 88 via weak lensing of standard sirens, expanding the cosmological insights obtainable from gravitational wave observations.

Findings

A 10% measurement of 88 is feasible with ET and 300 neutron star binaries.

LISA can measure 88 with 30% accuracy using 12 massive black hole binaries.

Weak lensing provides a new avenue to constrain cosmic structure parameters independently.

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 $10\%$ measurement of $\sigma_8$ would be feasible with ET, provided a population of $300$ neutron star binaries with electromagnetic counterparts is observed. With LISA, the measurement of $\sigma_8$ would have $30\%$ accuracy, assuming a population of $12$ massive black hole binaries with electromagnetic counterparts is observed.