Degenerate higher derivative theories beyond Horndeski: evading the Ostrogradski instability

DHOST theories generalize Horndeski and beyond-Horndeski models and are the most general class of ghost-free scalar-tensor theories.

“They generalize Horndeski and beyond-Horndeski models and are the most general class of ghost-free scalar–tensor theories.”

Langlois et al. (2018) showed mimetic gravity theories can be formulated as DHOST with extra local gauge symmetry; they study linear perturbations and find they have either gradient instabilities or Ostrogradsky type instability in scalar sector coupled to matter.

“However, a very recent study Langlois et al. (2018) showed that mimetic gravity theories can be viewed/formulated as degenerate higher-order scalar theories (DHOST) (Langlois and Noui 2016a) with an extra local gauge symmetry. They study linear perturbations about a homogeneous and isotropic background for all mimetic theories and find that they have either gradient instabilities or an Ostrograd”

In DHOST theories, in vacuum absence of matter coupling, a special degeneracy of the Lagrangian ensures absence of ghosts even if equations of motion are higher order.

“In these theories, it was shown in the vacuum in absence of matter coupling that the presence of a special degeneracy of the Lagrangian ensures the absence of ghosts even if the equations of motion are higher order.”

Langlois and Noui (2016a, b) identified degeneracy conditions that assure theory is free from Ostrogradsky ghost even if equations of motion have higher order derivatives.

“Remarkably, Langlois and Noui (2016a, b) identified the degeneracy conditions that assure that the theory is free from Ostrogradsky ghost even if their equations of motion have higher order derivatives.”