Galileon gravity and its relevance to late time cosmic acceleration

We consider the covariant Galileon gravity taking into account the third order and fourth order scalar field Lagrangians L3(π) and L4(π), consisting of three and four π's with four and five derivatives acting on them, respectively. The background dynamical equations are set up for the system under consideration and the stability of the self-accelerating solution is demonstrated in a general setting. We extended this study to the general case of the fifth order theory. For the spherically symmetric static background, we spell out conditions for the suppression of fifth force effects mediated by the Galileon field π. We study field perturbations in the fixed background and investigate the conditions for their causal propagation. We also briefly discuss metric fluctuations and derive an evolution equation for matter perturbations in Galileon gravity.