Degenerate higher derivative theories beyond Horndeski: evading the Ostrogradski instability

Understand

Theories with higher order time derivatives generically suffer from ghost-like instabilities, known as Ostrogradski instabilities.

• This fate can be avoided by considering "degenerate" Lagrangians, whose kinetic matrix cannot be inverted, thus leading to constraints between canonical variables and a reduced number of physical degrees of freedom.
• In this work, we derive in a systematic way the degeneracy conditions for scalar-tensor theories that depend quadratically on second order derivatives of a scalar field.
• We thus obtain a classification of all degenerate theories within this class of scalar-tensor theories.