The parameter space of cubic Galileon models for cosmic acceleration

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, the other 90% being 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.