Modified first-order Horava-Lifshitz gravity: Hamiltonian analysis of the general theory and accelerating FRW cosmology in power-law F(R) model

Understand

We propose the most general modified first-order Ho\v{r}ava-Lifshitz (HL) gravity, whose action does not contain time derivatives higher than the second order.

• The Hamiltonian structure of this theory is studied in all the details in the case of the spatially-flat FRW space-time, demonstrating many of the features of the general theory.
• It is shown that, with some plausible assumptions, including the projectability of the lapse function, this model is consistent.
• As a large class of such theories, the modified HL $F(R)$ gravity is introduced.