Metric-affine bumblebee gravity: classical aspects

We consider the metric-affine formulation of bumblebee gravity, derive the field equations, and show that the connection can be written as Levi-Civita of a disformally related metric in which the bumblebee field determines the disformal part. As a consequence, the bumblebee field gets coupled to all the other matter fields present in the theory, potentially leading to nontrivial phenomenological effects. To explore this issue we compute the post-Minkowskian, weak-field limit and study the resulting effective theory. In this scenario, we couple scalar and spinorial matter to the effective metric, and then we explore the physical properties of the VEV of the bumblebee field, focusing mainly on the dispersion relations and the stability of the resulting effective theory.

Automated summary

In this study, the metric-affine formulation of bumblebee gravity is considered, field equations are derived, and it is shown that the bumblebee field becomes coupled to other matter fields with potential nontrivial effects. By computing the post-Minkowskian, weak-field limit, the resulting effective theory is explored, coupling scalar and spinorial matter to the effective metric and investigating the physical properties of the VEV of the bumblebee field, focusing on dispersion relations and stability.