Ostrogradsky mode in scalar-tensor theories with higher-order derivative couplings to matter

Understand

A metric transformation is a tool to find a new theory of gravity beyond general relativity.

• The gravity action is guaranteed to be free from a dangerous Ostrogradsky mode as long as the metric transformation is regular and invertible.
• Various degenerate higher-order scalar-tensor theories (DHOST) without extra degrees of freedom have been found through the metric transformation with a scalar field and its derivatives.
• In this work, we examine how a matter coupling changes the degeneracy for a theory generated from the Horndeski theory through the metric transformation with the second derivative of a scalar field, taking a minimally-coupled free scalar field as the matter field.