  We study how the dynamical vector degree of freedom in modified gravity
affects the CMB B-mode polarization in terms of the Einstein-aether theory. In
this theory, vector perturbations can be generated from inflation, which can
grow on superhorizon scales in the subsequent epochs and thereby leaves
imprints on the CMB B-mode polarization. We derive the linear perturbation
equations in a covariant formalism, and compute the CMB B-mode polarization
using the CAMB code modified so as to incorporate the effect of the aether
vector field. We find that the amplitude of the B-mode signal from the aether
field can surpass the contribution from the inflationary gravitational waves
for a viable range of model parameters. We also give an analytic argument
explaining the shape of the spectrum based on the tight coupling approximation.
