# Role of matter in gravitation: going beyond the Einstein-Maxwell theory

## TL;DR

This paper explores how matter interacts with gravity beyond Einstein-Maxwell theory by using multiple geometries, revealing new vector-tensor theories and potential applications in early universe cosmology.

## Contribution

It introduces a novel approach using Bekenstein's multiple geometries to generate new vector-tensor theories with matter interactions in curved spacetime.

## Key findings

- New vector-tensor theories from multiple geometries
- Reduction of high-derivative terms via auxiliary variables
- Potential implications for early universe models

## Abstract

For field theories in curved spacetime, defining how matter gravitates is part of the theory building process. In this letter, we adopt Bekenstein's multiple geometries approach to allow part of the matter sector to follow the geodesics on a general pseudo-Riemannian geometry, constructed from a tensor and a $U(1)$ gauge field. This procedure allows us to generate a previously unknown corner of vector-tensor theories. In the Jordan frame, apparent high-derivative terms of the vector field are reduced by integrating out an auxiliary variable, at the cost of introducing new matter interactions. As a simple example, we consider a conformal relation between different geometries and demonstrate the presence of an auxiliary degree. We conclude with a discussion of applications, in particular for the early universe.