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

• Received 2 January 2019

DOI:https://doi.org/10.1103/PhysRevD.99.044050