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.
