Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2010-06-16
Phys.Lett.B693:404-414,2010
Physics
High Energy Physics
High Energy Physics - Theory
LaTeX 18 pages. v2: added and updated references, improved Introduction, few minor corrections in presentation
Scientific paper
10.1016/j.physletb.2010.08.061
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. These problems are compared with those found in the original Ho\v{r}ava-Lifshitz gravity. A general observation on the structure of the Poisson bracket of Hamiltonian constraints in all theories of the Ho\v{r}ava-Lifshitz type is made: in the resulting tertiary constraint the highest order spatial derivative of the lapse $N$ is always of uneven order. Since the vanishing of the lapse (N=0) is required by the preservation of the Hamiltonian constraints under time evolution, we conclude that the non-projectable version of the theory is physically inconsistent.
Chaichian Masud
Oksanen Markku
Tureanu Anca
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