Generalized multi-Proca fields

TL;DR

This paper generalizes derivative self-interactions for multiple massive vector fields, ensuring the correct degrees of freedom, and explores their potential cosmological applications with new isotropic solutions.

Contribution

It introduces a systematic construction of multi-Proca interactions, including genuine multi-field terms and their non-minimal gravity couplings, expanding the framework beyond single vector field theories.

Findings

Identifies two classes of interactions: extended Proca and genuine multi-Proca.

Constructs new isotropic cosmological solutions with three vector fields.

Proposes a novel configuration combining previous solutions for unexplored cosmological scenarios.

Abstract

We extend previous results on healthy derivative self-interactions for a Proca field to the case of a set of massive vector fields. We obtain non-gauge invariant derivative self-interactions for the vector fields that maintain the appropriate number of propagating degrees of freedom. In view of the potential cosmological applications, we restrict to interactions with an internal rotational symmetry. We provide a systematical construction order by order in derivatives of the fields and making use of the antisymmetric Levi-Civita tensor. We then compare with the one single vector field case and show that the interactions can be broadly divided into two groups, namely the ones obtained from a direct extension of the generalized Proca terms and genuine multi-Proca interactions with no correspondence in the single Proca case. We also discuss the curved spacetime version of the interactions to include the necessary non-minimal couplings to gravity. Finally, we explore the cosmological applications and show that there are three different vector fields configurations giving rise to isotropic solutions. Two of them have already been considered in the literature and the third one, representing a combination of the first two, is new and offers unexplored cosmological scenarios.