Polarizations of gravitational waves in the bumblebee gravity model

Lorentz violation modifies the dispersion relation of gravitational waves (GWs), and induces birefringence anisotropy in propagation. Our study shows that can also activate multiple polarizations GWs. We use gauge invariants to investigate GWs bumblebee gravity model, obtain following results. (i) For a vector background ${b}^{\ensuremath{\mu}}$ with only nonzero temporal component ${b}^{t}$, there are five independent propagating degrees freedom (d.o.f.), which is similar Einstein-\ae{}ther theory. (ii) The presence spatial defines preferred direction breaks rotational symmetry. denote $\stackrel{^}{\mathbit{b}}$ as part ${b}_{s}$ its length. If propagate along $\stackrel{^}{\mathbit{b}}$, polarization content purely timelike case. (iii) propagation separated by an angle $\ensuremath{\beta}$ $\ensuremath{\beta}=\mathrm{arccos}({b}^{t}/{b}_{s})$, two tensor polarizations. (iv) $\ensuremath{\beta}\ensuremath{\ne}\mathrm{arccos}({b}^{t}/{b}_{s})$, d.o.f., scalar modes degenerate modes. perturbations mixture all six simultaneously. Finally, we point out difference between model minimal Standard-Model Extension framework linearized regime. Current observations have placed stringent constraints on induced background, while our theoretical still reveals some novel phenomena provides more understanding about interaction Lorentz-violating field gravity.