Coupled multi-Proca vector dark energy

We study a new class of vector dark energy models where multi-Proca fields $A_\mu^a$ are coupled to cold matter by the term $f(X)\tilde{\mathcal{L}}_{m}$ $f(X)$ is general function $X\equiv -\frac{1}{2}A^\mu_ A^a_\mu$ and $\tilde{\mathcal{L}}_{m}$ Lagrangian. From here, we derive covariant form novel interaction sourcing field equations. This result quite in sense that encompasses Abelian non-Abelian fields. In particular, investigate effects this type coupling simple model based on three copies canonical Maxwell realize isotropic expansion. The cosmological background dynamics examined means dynamical system analysis determine stability emergent solutions. As an interesting result, find leads existence scaling solution during dominance. Furthermore, critical points show early contribution radiation stable de Sitter-type attractor at late times mimicking energy. evolution as well aforementioned features verified numerical computations. Observational constraints also discussed put more phenomenological context light future observations.