Scalar-tensor theory with EGB term from Einstein Chern-Simons gravity

It is shown that the compactification a la Randall Sundrum of the so called, five dimensional Einstein Chern Simons action gravity leads to an action for a four dimensional scalar tensor gravity that includes a Gauss Bonnet term, which belongs to a particular case of the action of the Horndeski theory. The five dimensional action includes new gravitational degrees of freedom that were introduced requiring that the action be invariant under symmetries greater than the usual Poincare or (A)dS symmetries, namely the so called generalized Poincare algebras B5.