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 non-linear derivative interaction for the scalar
field. Such an additional scalar degree of freedom is called "Galileon". The
basic idea is inspired by the DGP 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 $\Lambda$CDM
cosmology, the behavior of perturbation is quite different. It is shown that
there exists a super-horizon 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 DGP model.
