Higgs mechanism
The possibility that a gravitational Higgs mechanism in bumblebee models could endow the graviton with mass was considered by Kostelecky and Samuel. They showed, however, that what appears to be a mass term involves the square of the affine connection formula_32. Since the connection is a function of derivatives of the metric, this cannot be a mass term. Thus, there is no conventional Higgs mechanism in bumblebee models that results in a massive graviton.