  Gravitational particle production of spectator fields due to the expansion
universe during the inflationary and reheating phases of the early universe is
of particular interest in the context of dark matter, since it allows to
constrain the properties of the dark candidate by comparing the density of
particles produced with the observed dark matter abundance. In such processes,
tachyonic instabilities arise as a consequence of the coupling to the
curvature, greatly enhancing mode production. In this work, we consider a
massive vector field that is coupled to the curvature scalar and the Ricci
tensor only, and study its gravitational production through inflation and
reheating. We show how the mechanism is more efficient than in the case of a
non-minimally coupled scalar field, giving rise to larger abundances. Moreover,
we analyze the importance of the coupling to the Ricci tensor, which increases
tachyonic instabilities in the system, and constrain the mass of the dark
particle and the values of the coupling constants by comparing the
corresponding abundance with observations
