Modified F(R) Horava-Lifshitz gravity: a way to accelerating FRW cosmology

TL;DR

This paper develops a modified F(R) Hořava-Lifshitz gravity framework that maintains foliation-preserving diffeomorphism invariance, capable of unifying early inflation and late-time cosmic acceleration, and aligns with traditional F(R) gravity under specific parameters.

Contribution

It introduces a general, diffeomorphism-invariant modified gravity approach, analyzes its Hamiltonian structure, and demonstrates its potential to unify different cosmic acceleration phases.

Findings

FRHL equations are consistent with constraints.

De Sitter solutions suggest unification of inflation and acceleration.

Special parameters recover traditional F(R) gravity equations.

Abstract

We propose a general approach for the construction of modified gravity which is invariant under foliation-preserving diffeomorphisms. Special attention is paid to the formulation of modified $F(R)$ Ho\v{r}ava-Lifshitz gravity (FRHL), whose Hamiltonian structure is studied. It is demonstrated that the spatially-flat FRW equations of FRHL are consistent with the constraint equations. The analysis of de Sitter solutions for several versions of FRHL indicates that the unification of the early-time inflation with the late-time acceleration is possible. It is shown that a special choice of parameters for FRHL leads to the same spatially-flat FRW equations as in the case of traditional $F(R)$-gravity. Finally, an essentially most general modified Ho\v{r}ava-Lifshitz gravity is proposed, motivated by its fully diffeomorphism-invariant counterpart, with the restriction that the action does not contain derivatives higher than the second order with respect to the time coordinate.