Galileons in the sky

We review the different frameworks in which Galileon scalar fields have been seen to emerge such as in DGP, New Massive Gravity and Ghost-free Massive Gravity and emphasize their relation with the Lovelock invariant in braneworld models. The existence of a non-renormalization theorem for Galileon scalar fields makes them especially attractive candidates for inflation as well as for late-time acceleration. In particular, we review the self-accelerating and degravitating branches of solutions present in Galileon models when arising from Massive Gravity and discuss their phenomenology. (c) 2012 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.