B-mode polarization in Einstein-aether theory

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 be larger than the contribution from the inflationary gravitational waves for reasonable initial conditions and for a viable range of model parameters, in which perturbation modes propagate superluminally. We also give an analytic argument explaining the shape of the spectrum based on the tight coupling approximation.