Imprint of ultralight vector fields on gravitational wave propagation

We study the effects of ultralight vector field (ULVF) dark matter on gravitational wave propagation. We find that the coherent oscillations of the vector field induce an anisotropic suppression of the gravitational wave amplitude as compared to the $\Lambda$CDM prediction. The effect is enhanced for smaller vector field masses and peaks for modes around $k=H_0/\sqrt{a(H=m)}$. The suppression is negligible for astrophysically generated gravitational waves but could be sizeable for primordial gravity waves. We discuss the possibility of detecting such an effect on the CMB B-mode power spectrum with the sensitivity of future detectors. We find that the upcoming LiteBIRD mission would be sensitive to ULVF dark matter with masses $m\lesssim 10^{-26}$ eV for sufficiently large abundances.