Phantom attractors in Kinetic Gravity Braiding theories: a dynamical system approach

We revise the expansion history of the scalar field theories known as Kinetic Gravity Braiding. These theories are well-known for the possibility of driving the expansion of the cosmos towards a future self-tuning de Sitter state when the corresponding Lagrangian is invariant under constant shifts in the scalar field. Nevertheless, this is not the only possible future fate of these shift-symmetric models. Using a dynamical system formulation we show that future cosmological singularities can also appear in this framework. Moreover, we present explicit examples where the future attractor in the configuration space of the theory corresponds to a big rip singularity.