Hamiltonian analysis of non-projectable modified F(R) Ho\v{r}ava-Lifshitz gravity

Understand

We study a version of the recently proposed modified $F(R)$ Ho\v{r}ava-Lifshitz gravity that abandons the projectability condition of the lapse variable.

• We discovered that the projectable version of this theory has a consistent Hamiltonian structure, and that the theory has interesting cosmological solutions which can describe the eras of accelerated expansion of the universe in a unified manner.
• The usual Ho\v{r}ava-Lifshitz gravity is a special case of our theory.
• Hamiltonian analysis of the non-projectable theory, however, shows that this theory has serious problems.