  The generalised Proca (GP) theory is a modified gravity model in which the
acceleration of the cosmic expansion rate can be explained by self interactions
of a cosmological vector field. In this paper we study a particular sub-class
of the GP theory, with up to cubic order Lagrangian, known as the cubic vector
Galileon (cvG) model. This model is similar to the cubic scalar Galileon (csG)
in many aspects, including a fifth force and the Vainshtein screening
mechanism, but with the additional flexibility that the strength of the fifth
force depends on an extra parameter -- interpolating between zero and the full
strength of the csG model -- while the background expansion history is
independent of this parameter. It offers an interesting alternative to
LambdaCDM in explaining the cosmic acceleration, as well as a solution to the
tension between early- and late-time measurements of the Hubble constant H_0.
To identify the best ways to test this model, in this paper we conduct a
comprehensive study of the phenomenology of this model in the nonlinear regime
of large-scale structure formation, using a suite of N-body simulations run
with the modified gravity code ECOSMOG. By inspecting thirteen statistics of
the dark matter field, dark matter haloes and weak lensing maps, we find that
the fifth force in this model can have particularly significant effects on the
large-scale velocity field and lensing potential at late times, which suggest
that redshift-space distortions and weak lensing can place strong constraints
on it.
