Degenerate higher order scalar-tensor theories of gravity and observational constraints
The degenerate higher order scalar-tensor (DHOST) theories are the general scalar-tensor theories of gravity without Ostrogradsky instabilities which the action contains the terms up to cubic in second order derivatives of a scalar field. Basic of Ostrogradsky instabilities and degeneracy conditions for avoiding these instabilities can be understood in the contexts of classical mechanics and quantum theory. Based on the symmetry of second order derivatives of a scalar field, the general form of the gravity action containing the terms quadratic and cubic in second order derivatives of a scalar field can be constructed. Applying the degeneracy conditions to the resulting action, the DHOST theories are obtained. the DHOST theories are stringently constrained from the requirement that the gravitational waves (GW) propagate at the speed of light as measured by recent GW detection. Possible constraints from astrophysical objects, Cosmic Microwave Background and growth of density perturbations are also discussed.