2025/07/27 by Wang, Ke
#Cosmology and Nongalactic Astrophysics (astro-ph.CO) #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc)
paper · doi:10.48550/arxiv.2507.20323
The Schrödinger-Poisson (SP) equations predict fuzzy dark matter (FDM) solitons. Given the FDM mass ∼10-20\rm~eV/c2, the FDM soliton in the Milky Way is massive ∼ 107~M\odot but diffuse ∼ 10\rm~pc. Therefore, this FDM soliton can serve as a gravitational lens for gravitational waves (GWs) with frequency ∼10-8\rm~Hz. In this paper, we investigate its gravitational lensing effects by numerical simulation of the propagation of GWs through it. We find that the maximum magnification factor of GWs is very small ∼10-4, but the corresponding magnification zone is huge ∼6\rm~pc for FDM with mass equal to 8-21\rm~eV/c2. Consequently, this small magnification factor in that large magnification zone means a small antisotropy of ∼10-4 over a large solid angle in the GW background, even though this antisotropy is out of the sensitivity of the pulsar timing arrays today.