Self-Accelerating Universe in Galileon Cosmology

We present a cosmological model with a solution that self-accelerates at late-times without signs of ghost instabilities on small scales. The model is a natural extension of the Brans-Dicke (BD) theory including a non-linear derivative interaction, which appears in a theory with the Galilean shift symmetry. The existence of the self-accelerating universe requires a negative BD parameter but, thanks to the non-linear term, small fluctuations around the solution are stable on small scales. General relativity is recovered at early times and on small scales by this non-linear interaction via the Vainshtein mechanism. At late time, gravity is strongly modified and the background cosmology shows a phantom-like behaviour and the growth rate of structure formation is enhanced. Thus this model leaves distinct signatures in cosmological observations and it can be distinguished from standard $\mathrm{\Lambda }$CDM cosmology.