Emergent universe in Horava-Lifshitz-like F(R) gravity
  We investigate the Einstein static universe (ESU) and the emergent universe
scenario in the framework of Ho\v{r}ava-Lifshitz-like $F(R)$ gravity. We first
perform a dynamical analysis in the phase space, and amongst others we show
that a spatially open universe filled with matter satisfying the strong energy
condition can exhibit a stable static phase. Additionally, we examine the
behavior of the scenario under scalar perturbations and extract the conditions
under which it is free of perturbative instabilities, showing that the obtained
background ESU solutions are free of such instabilities. However, in order for
the Einstein static universe to give rise to the emergent universe scenario we
need to have an exotic matter sector that can lead the universe to depart from
the stable static state and enter into its usual expanding thermal history.
