U(1) Invariant F(R) Horava-Lifshitz Gravity

TL;DR

This paper explores U(1) invariant F(R) Horava-Lifshitz gravity, demonstrating its stability properties, Hamiltonian structure, and cosmological solutions, thereby extending the theoretical framework and analyzing its physical consistency.

Contribution

It formulates a U(1) extension of F(R) HL gravity, develops its Hamiltonian structure, and analyzes its stability and cosmological solutions, advancing the understanding of this modified gravity theory.

Findings

Stable de Sitter solutions exist in some versions.

Flat space solutions are unstable, avoiding scalar graviton issues.

The theory's spectrum includes only transverse graviton polarization.

Abstract

This paper is devoted to the study of various aspects of projectable F(R) Horava-Lifshitz (HL) gravity. We show that some versions of F(R) HL gravity may have stable de Sitter solution and instable flat space solution. In this case, the problem of scalar graviton does not appear because flat space is not vacuum state. Generalizing the U(1) HL theory proposed in arXiv:1007.2410, we formulate U(1) extension of scalar theory and of F(R) Horava-Lifshitz gravity. The Hamiltonian approach for such the theory is developed in full detail. It is demonstrated that its Hamiltonian structure is the same as for the non-relativistic covariant HL gravity. The spectrum analysis performed around flat background indicates towards the consistency of the theory because it contains graviton with only transverse polarization. Finally, we analyze the spatially-flat FRW equations for U(1) invariant F(R) Horava-Lifshitz gravity.