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We investigate the nonlinear growth of large-scale structure in thegeneralised Proca theory, in which a self-interacting massive vector fieldplays the role of driving the acceleration of the cosmic expansion. Focusing tothe Proca Lagrangian at cubic order -- the cubic vector Galileon model -- wederive the simplified equations for gravity as well as the longitudinal andtransverse modes of the vector field under the weak-field and quasi-staticapproximations, and implement them in a modified version of the ECOSMOG N-bodycode. Our simulations incorporate the Vainshtein screening effect, whichreconciles the fifth force propagated by the longitudinal mode of the cubicvector Galileon model with local tests of gravity. The results confirm that forall scales probed by the simulation, the transverse mode has a negligibleimpact on structure formation in a realistic cosmological setup. It is wellknown that in this model the strength of the fifth force is controlled by afree model parameter, which we denote as beta_3. By running a suite ofcosmological simulations for different values of beta_3, we show that thisparameter also determines the effectiveness of the Vainshtein screening. Themodel behaves identically to the cubic scalar Galileon for beta_3 going tozero, in which the fifth force is strong in unscreened regions but isefficiently screened in high-density regions. In the opposite limit, beta_3going to infinity, the model approaches its `quintessence' counterpart, whichhas a vanishing fifth force but a modified expansion history compared toLambdaCDM. This endows the model with rich phenomenology, which will beinvestigated in future works.

Proca-stinated Cosmology I: A N-body code for the vector Galileon