The Vector-Tensor nature of Bekenstein's relativistic theory of Modified Gravity

TL;DR

This paper demonstrates that Bekenstein's relativistic modified gravity theory can be reformulated as a Vector-Tensor theory similar to Einstein-Aether models, revealing new insights into its structure and implications.

Contribution

It shows the equivalence between Bekenstein's bi-metric theory and a Vector-Tensor framework, providing a new perspective on its formulation.

Findings

Reformulation of Bekenstein's theory as Vector-Tensor theory

Identification of similarities with Einstein-Aether models

Discussion of implications of the equivalence

Abstract

Bekenstein's theory of relativistic gravity is conventionally written as a bi-metric theory. The two metrics are related by a disformal transformation defined by a dynamical vector field and a scalar field. In this comment we show that the theory can be re-written as Vector-Tensor theory akin to Einstein-Aether theories with non-canonical kinetic terms. We discuss some of the implications of this equivalence.