Polarizations of gravitational waves in the bumblebee gravity model

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', there are five independent propagating degrees of freedom (d.o.f.), which is similar to the Einstein-nether theory. (ii) The presence of a spatial component in the background defines a preferred spatial direction which breaks rotational symmetry. We denote b as the direction of the spatial part of the background and bs as its length. If GWs propagate along b, the polarization content is similar to the purely timelike case. (iii) If the propagation direction of GWs is separated by an angle /3 to b, and independent d.o.f., 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. Current observations have placed stringent constraints on the anisotropy induced by the background, while our theoretical study still reveals some novel phenomena and provides more understanding about the interaction between the Lorentz-violating vector field and gravity.

Automated summary

This study reveals the effects of Lorentz violation on gravitational waves, including modifications to their dispersion relation, induction of birefringence and anisotropy in propagation. The researchers used gauge invariants to investigate the polarizations of gravitational waves in the bumblebee gravity model and found multiple polarizations. They also discussed the differences between the bumblebee gravity model and the minimal Standard-Model Extension framework in the linearized regime.