Constructing degenerate higher-order theories

Scalar-tensor theories serve models for inflation and dark energy. Many efforts have been made recently for constructing the most general scalar-tensor theories with higher-order derivatives in their Lagrangian. Since higher-derivative theories are typically associated with Ostrogradsky ghost which causes unbounded Hamiltonian, it is important to clarify how to evade it. In this talk, I will explain construction of healthy degenerate theories with higher-order derivatives which circumvent Ostrogradsky ghost.  The method also allows us to construct ghost-free theories with derivatives higher than second order in Lagrangian.