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

A scalar-tensor theory of gravity can be made not only to account for the current cosmic acceleration, but also to satisfy solar-system and laboratory constraints, by introducing a nonlinear derivative interaction for the scalar field. Such an additional scalar degree of freedom is called ``Galileon. '' The basic idea is inspired by the Dvali-Gabadadze-Porrati braneworld, but one can construct a ghost-free model that admits a self-accelerating solution. We perform a fully relativistic analysis of linear perturbations in Galileon cosmology. Although the Galileon model can mimic the background evolution of standard cosmology, the behavior of perturbation is quite different. It is shown that there exists a superhorizon growing mode in the metric and Galileon perturbations at early times, suggesting that the background is unstable. A fine-tuning of the initial condition for the Galileon fluctuation is thus required in order to promote a desirable evolution of perturbations at early times. Assuming the safe initial condition, we then compute the late-time evolution of perturbations and discuss observational implications in Galileon cosmology. In particular, we find anticorrelations in the cross correlation of the integrated Sachs-Wolfe effect and large scale structure, similar to the normal branch of the Dvali-Gabadadze-Porrati model.