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An alternative for the construction of fundamental theories is the introduction of Galileons. These are fields whose action leads to non higher than second-order equations of motion. As this is a necessary but not sufficient condition to make the Hamiltonian bounded from below, as long as the action is not degenerate, the Galileon construction is a way to avoid pathologies both at the classical and quantum levels. Galileon actions are, therefore, of great interest in many branches of physics, specially in high energy physics and cosmology. This proceedings contribution presents the generalities of the construction of both scalar and vector Galileons following two different but complimentary routes.
In the context of a cubic Galileon model in which the Vainshtein mechanism suppresses the scalar field interactions with matter, we study low-density stars with slow rotation and static relativistic stars. We develop an expansion scheme to find appro
The Vainshtein screening mechanism relies on nonlinear interaction terms becoming dominant close to a compact source. However, theories displaying this mechanism are generally understood to be low-energy theories: it is unclear that operators emergin
Vector theories with non-linear derivative self-interactions that break gauge symmetries have been shown to have interesting cosmological applications. In this paper we introduce a way to spontaneously break the gauge symmetry and construct these the
Vector Galileons are ghost-free systems containing higher derivative interactions of vector fields. They break the vector gauge symmetry, and the dynamics of the longitudinal vector polarizations acquire a Galileon symmetry in an appropriate decoupli
We have investigated if the vector field can give rise to an accelerating phase in the early universe. We consider a timelike vector field with a general quadratic kinetic term in order to preserve an isotropic background spacetime. The vector field