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.

我们考虑了大黄蜂重力的度量仿射公式，推导出了场方程，并表明该连接可以写为变形相关度量的Levi-Civita，其中大黄蜂场决定了变形部分。结果，大黄蜂场与理论中存在的所有其他物质场耦合，可能导致非平凡的现象学效应。为了探讨这个问题，我们计算了后Minkowskian的弱场极限，并研究了由此产生的有效理论。在这种情况下，我们将标量和脊髓物质耦合到有效量度，然后我们研究大黄蜂场的VEV的物理特性，主要集中在色散关系和所得有效理论的稳定性上。