# On scalar and vector fields coupled to the energy-momentum tensor

## TL;DR

This paper develops a systematic approach to constructing theories where scalar and vector fields are coupled to the energy-momentum tensor, leading to self-interactions and novel phenomenological implications, including constraints from observations.

## Contribution

It introduces an iterative method to build coupled field theories, extends analysis to derivative couplings, and explores vector field interactions with matter and boundary term ambiguities.

## Key findings

- Derived solutions as infinite series and polynomials.
- Extended scalar field models to include disformal couplings.
- Set observational constraints on coupling parameters.

## Abstract

We consider theories for scalar and vector fields coupled to the energy-momentum tensor. Since these fields also carry a non-trivial energy-momentum tensor, the coupling prescription generates self-interactions. In analogy with gravity theories, we built the action by means of an iterative process that leads to an infinite series, which can be resumed as the solution of a set of differential equations. We show that, in some particular cases, the equations become algebraic and that is also possible to find solutions in the form of polynomials. We briefly review the case of the scalar field that has already been studied in the literature and extend the analysis to the case of derivative (disformal) couplings. We then explore theories with vector fields, distinguishing between gauge- and non-gauge-invariant couplings. Interactions with matter are also considered, taking a scalar field as a proxy for the matter sector. We also discuss the ambiguity introduced by superpotential (boundary) terms in the definition of the energy-momentum tensor and use them to show that it is also possible to generate Galileon-like interactions with this procedure. We finally use collider and astrophysical observations to set constraints on the dimensionful coupling which characterises the phenomenology of these models.