Ghost-free Gauss-Bonnet Theories of Gravity
  In this work we develop a theoretical framework for Gauss-Bonnet modified
gravity theories, in which ghost modes can be eliminated at the equations of
motion level. Particularly, after we present how the ghosts can occur at the
level of equations of motion, we employ the Lagrange multipliers technique, and
by means of constraints we are able to eliminate the ghost modes from
Gauss-Bonnet theories of the form $f(\mathcal{G})$ and $F(R,\mathcal{G})$
types. Some cosmological realizations in the context of the ghost free
$f(\mathcal{G})$ gravity are presented, by using the reconstruction technique
we developed. Finally, we explore the modifications to the Newton law of
gravity generated by the ghost-free $f(\mathcal{G})$ theory.
