Amplitude and Phase Fluctuations for Gravitational Waves Propagating through Inhomogeneous Mass Distribution in the Universe

Abstract

When a gravitational wave (GW) propagates through the universe, its amplitude and phase change due to gravitational lensing by the inhomogeneous mass distribution. We derive the amplitude and phase fluctuations, and calculate these variances in the limit of a weak gravitational field of density perturbation. We find that (1) the rms amplitude fluctuation is 1 – 10% for f > 10−10 Hz, but it is reduced less than 5% for a very low frequency of f < 10−12 Hz, (2) the rms phase fluctuation in the chirp signal is ∼ 10−3 radian at LISA frequency band.