A covariant Lagrangian for stable nonsingular bounce

The nonsingular bounce models usually suffer from the ghost or gradient instabilities, as has been proved recently. In this paper, we propose a covariant effective theory for stable nonsingular bounce, which has the quadratic order of the second order derivative of the field phi but the background set only by P(phi, X). With it, we explicitly construct a fully stable nonsingular bounce model for the ekpyrotic scenario.