Detailed balance in Hǒrava–Lifshitz gravity

We study Hořava–Lifshitz gravity in the presence of a scalar field. When the detailed balance condition is implemented, a new term in the gravitational sector is added in order to maintain ultraviolet stability. The four-dimensional theory is of scalar-tensor type with a positive cosmological constant and gravity is non-minimally coupled with the scalar and its gradient terms. The scalar field has a double-well potential and, if required to play the role of the inflation, can produce a scaleinvariant spectrum. The total action is rather complicated and there is no analog of the Einstein frame where Lorentz invariance is recovered in the infrared. For these reasons it may be necessary to abandon detailed balance. We comment on open problems and future directions in anisotropic critical models of gravity.