Metric-affine bumblebee gravity: classical aspects

TL;DR

This paper investigates the metric-affine formulation of bumblebee gravity, deriving the field equations and analyzing the weak-field limit to understand how the bumblebee field influences matter coupling and phenomenology.

Contribution

It introduces a novel formulation where the connection relates to a disformally transformed metric driven by the bumblebee field, affecting matter interactions.

Findings

Connection expressed as Levi-Civita of a disformally related metric

Bumblebee field couples to matter, influencing dispersion relations

Analysis of stability and phenomenological implications in the weak-field limit

Abstract

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 weak-field, post-Minkowskian 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.