Cosmic expansion and growth histories in Galileon scalar-tensor models of dark energy

We study models of late-time cosmic acceleration in terms of scalar-tensor theories generalized to include a certain class of nonlinear derivative interaction of the scalar field. The nonlinear effect suppresses the scalar-mediated force at short distances to pass solar-system tests of gravity. It is found that the expansion history until today is almost indistinguishable from that of the Lambda CDM model or some (phantom) dark energy models, but the fate of the universe depends clearly on the model parameter. The growth index of matter density perturbations is computed to show that its past asymptotic value is given by 9/16, while the value today is as small as 0.4.