Tracking our Universe to de Sitter by a Horndeski scalar
  Assuming both that our Universe is evolving into a de Sitter space and a
vanishing cosmological constant, leaves only the option that the observed
acceleration is provided by a "kinetic" energy of a scalar field. From an
effective field theory point of view, the absence of Ostrogradsky instabilities
restricts the choice to shift-symmetric Horndeski theories. Within these
theories, we find the conditions for the existence of a de Sitter critical
point in a universe filled by matter, radiation and a Horndeski scalar.
Moreover, we show that this point is a universal attractor and we provide the
tracking trajectory. Therefore, if a de Sitter fixed point exists within these
models, our Universe will eventually evolve into a de Sitter space. As an
example, we have discussed the case of the combined Galileon-Slotheon system,
in which the Galileon is kinetically non-minimal coupled to the Einstein
tensor. Interestingly, we have also found that the tracker trajectory of this
system does not follow previous literature assumptions.
