$f(R)$ theory and geometric origin of the dark sector in Horava-Lifshitz gravity

TL;DR

This paper explores an extended Horava-Lifshitz gravity model incorporating an $f(R)$ term, revealing a geometric origin for dark matter and dark energy, and analyzing stability and cosmological solutions.

Contribution

It introduces an $f(R)$ extension to Horava-Lifshitz gravity without detailed balance, showing how dark sectors can emerge geometrically and examining stability conditions.

Findings

Dark sector has a geometric origin in the model.

Scalar mode stability depends on background curvature.

Bouncing universe solutions are possible.

Abstract

Inclusion of $f(R)$ term in the action of Horava-Lifshitz quantum gravity with projectability but without detailed balance condition is investigated, where $R$ denotes the 3-spatial dimensional Ricci scalar. Conditions for the spin-0 graviton to be free of ghosts and instability are studied. The requirement that the theory reduce to general relativity in the IR makes the scalar mode unstable in the Minkowski background but stable in the de Sitter. It is remarkable that the dark sector, dark matter and dark energy, of the universe has a naturally geometric origin in such a setup. Bouncing universes can also be constructed. Scalar perturbations in the FRW backgrounds with non-zero curvature are presented.