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A scalar-tensor theory of gravity can be made not only to account for thecurrent cosmic acceleration, but also to satisfy solar-system and laboratoryconstraints, by introducing a non-linear derivative interaction for the scalarfield. Such an additional scalar degree of freedom is called "Galileon". Thebasic idea is inspired by the DGP braneworld, but one can construct aghost-free model that admits a self-accelerating solution. We perform a fullyrelativistic analysis of linear perturbations in Galileon cosmology. Althoughthe Galileon model can mimic the background evolution of standard $\Lambda$CDMcosmology, the behavior of perturbation is quite different. It is shown thatthere exists a super-horizon growing mode in the metric and Galileonperturbations at early times, suggesting that the background is unstable. Afine-tuning of the initial condition for the Galileon fluctuation is thusrequired in order to promote a desirable evolution of perturbations at earlytimes. Assuming the safe initial condition, we then compute the late-timeevolution of perturbations and discuss observational implications in Galileoncosmology. In particular, we find anticorrelations in the cross-correlation ofthe integrated Sachs-Wolfe effect and large scale structure, similar to thenormal branch of the DGP model.

Evolution of linear cosmological perturbations and its observational implications in Galileon-type modified gravity