Gravitational wave sources are a promising cosmological standard candle
because their intrinsic luminosities are determined by fundamental physics (and
are insensitive to dust extinction). They are, however, affected by weak
lensing magnification due to the gravitational lensing from structures along
the line of sight. This lensing is a source of uncertainty in the distance
determination, even in the limit of perfect standard candle measurements. It is
commonly believed that the uncertainty in the distance to an ensemble of
gravitational wave sources is limited by the standard deviation of the lensing
magnification distribution divided by the square root of the number of sources.
Here we show that by exploiting the non-Gaussian nature of the lensing
magnification distribution, we can improve this distance determination,
typically by a factor of 2--3; we provide a fitting formula for the effective
distance accuracy as a function of redshift for sources where the lensing noise
dominates.Comment: matches PRD accepted version (expanded description of the
cosmological parameter space + minor changes
