The 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 tensor power spectrum with future CMB B-mode polarization detectors. We find that for the sensitivity of the upcoming LiteBIRD mission, the correction to the tensor power spectrum at decoupling time could be distinguishable from that of $\Lambda$CDM for ULVF masses $m\lesssim 10^{-26}$ eV and sufficiently large abundances.