Comment on "Modified F(R) Ho\v{r}ava-Lifshitz gravity: a way to accelerating FRW cosmology" by M. Chaichian, S. Nojiri, S. D. Odintsov, M. Oksanen, A. Tureanu

TL;DR

This paper critiques a previous analysis of Hořava-Lifshitz gravity, clarifying that the algebra of constraints differs when using covariant shift variables instead of the usual contravariant shift, impacting the theoretical consistency.

Contribution

It provides a corrected algebra of constraints for Hořava-Lifshitz gravity with covariant shift variables, highlighting the importance of variable choice in Hamiltonian analysis.

Findings

Incorrect algebra of constraints identified in the original paper.

Correct algebra of constraints explicitly derived for covariant shift variables.

Comparison made with the standard algebra in General Relativity.

Abstract

The partial Hamiltonian analysis of the Ho\v{r}ava-type action presented in the paper by M. Chaichian, S. Nojiri, S. D. Odintsov, M. Oksanen, A. Tureanu (Class. Quant. Grav. 27 (2011) 185021) is incorrect; for the authors' choice of variables, a covariant shift, instead of a contravariant shift which is the one usually used in General Relativity (GR) in ADM variables, the true algebra of constraints differs from what they presented. The algebra of constraints for their choice of variables is explicitly given for GR and compared with the standard algebra.