  We use recent measurements of the expansion history of the universe to place
constraints on the parameter space of cubic Galileon models, in particular we
concentrate on those models which contain the simplest Galileon term plus a
linear potential. This gives strong constraints on the Lagrangian of these
models. Most dynamical terms in the Galileon Lagrangian are constraint to be
small and the acceleration is effectively provided by a constant term in the
scalar potential, thus reducing, effectively, to a LCDM model for current
acceleration. The effective equation of state is indistinguishable from that of
a cosmological constant w = -1 and the data constraint it to have no temporal
variations of more than at the few % level. The energy density of the Galileon
can contribute only to about 10% of the acceleration energy density, being the
other 90% a cosmological constant term. This demonstrates how useful direct
measurements of the expansion history of the universe are at constraining the
dynamical nature of dark energy.
