Kavli Affiliate: Lijing Shao
| First 5 Authors: Dicong Liang, Rui Xu, Xuchen Lu, Lijing Shao,
| Summary:
Lorentz violation modifies the dispersion relation of gravitational waves
(GWs), and induces birefringence and anisotropy in propagation. Our study shows
that Lorentz violation can also activate multiple polarizations of GWs. We use
the gauge invariants to investigate the polarizations of GWs in the bumblebee
gravity model, and obtain the following results. (i) For a vector background
$b^mu$ with only a nonzero temporal component $b^t$, there are five
independent propagating degrees of freedom (DOFs), which is simlar to the
Einstein-ae{}ther theory. (ii) The presence of a spatial component in the
background defines a preferred direction which breaks the rotation symmetry. We
denote $hat{bm{b}}$ as the direction of the spatial part of the background
and $b_s$ as its length. If GWs propagate along $hat{bm{b}}$, the
polarization content is similar to the purely timelike case. (iii) If the
propagation direction of GWs is separated by an angle $beta$ to
$hat{bm{b}}$, and $beta=arccos(b^t/b_s)$, there are only two tensor
polarizations. (iv) If $betaneq arccos(b^t/b_s)$, there are only two
independent DOFs, and the vector and scalar modes degenerate with the tensor
modes. The tensor perturbations can activate a mixture of all six polarizations
simultaneously. Finally, we point out the difference in GWs between the
bumblebee gravity model and the minimal Standard-Model Extension framework in
the linearized regime.
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