Gravitational Wave Sirens as a Triple Probe of Dark Energy

Gravitational wave standard sirens have been considered as precision distance indicators to high redshift; however, at high redshift standard sirens or standard candles such as supernovae suffer from lensing noise. We investigate lensing noise as a signal instead and show how measurements of the maximum demagnification (minimum convergence) probe cosmology in a highly complementary manner to the distance itself. Revisiting the original form for minimum convergence we quantify the bias arising from the commonly used approximation. Furthermore, after presenting a new lensing probability function we discuss how the width of the lensed standard siren amplitude distribution also probes growth of structure. Thus standard sirens and candles can serve as triple probes of dark energy, measuring both the cosmic expansion history and growth history.