Proca-stinated Cosmology I: A N-body code for the vector Galileon
  We investigate the nonlinear growth of large-scale structure in the
generalised Proca theory, in which a self-interacting massive vector field
plays the role of driving the acceleration of the cosmic expansion. Focusing to
the Proca Lagrangian at cubic order -- the cubic vector Galileon model -- we
derive the simplified equations for gravity as well as the longitudinal and
transverse modes of the vector field under the weak-field and quasi-static
approximations, and implement them in a modified version of the ECOSMOG N-body
code. Our simulations incorporate the Vainshtein screening effect, which
reconciles the fifth force propagated by the longitudinal mode of the cubic
vector Galileon model with local tests of gravity. The results confirm that for
all scales probed by the simulation, the transverse mode has a negligible
impact on structure formation in a realistic cosmological setup. It is well
known that in this model the strength of the fifth force is controlled by a
free model parameter, which we denote as beta_3. By running a suite of
cosmological simulations for different values of beta_3, we show that this
parameter also determines the effectiveness of the Vainshtein screening. The
model behaves identically to the cubic scalar Galileon for beta_3 going to
zero, in which the fifth force is strong in unscreened regions but is
efficiently screened in high-density regions. In the opposite limit, beta_3
going to infinity, the model approaches its `quintessence' counterpart, which
has a vanishing fifth force but a modified expansion history compared to
LambdaCDM. This endows the model with rich phenomenology, which will be
investigated in future works.
