In order to explain the accelerated expansion of our universe in its early stage and today, the most popular approach is to introduce a scalar field to drive the inflation or to act as dark energy. This is the so-called scalar-tensor theory of gravity. In this talk, the speaker will first review the development of the scalar-tensor theories with higher derivatives in recent years. Then he will introduce the idea of constructing gravity theories respecting only the spatial symmetry, which propagate a single scalar degree of freedom and thus correspond to even a larger class of healthy scalar-tensor theories with higher derivatives. Finally, he will also discuss the propagation of gravitational waves in the framework.
