Stability of Singularity-free Cosmological Solutions in   Ho\v{r}ava-Lifshitz Gravity
  We study stability of singularity-free cosmological solutions with positive cosmological constant based on projectable Ho\v{r}ava-Lifshitz (HL) theory. In HL theory, the isotropic and homogeneous cosmological solutions with bounce can be realized if spacial curvature is non-zero. By performing perturbation analysis around non-flat Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetime, we derive a quadratic action and discuss the stability, i.e, ghost and tachyon-free conditions. Although the squared effective mass of scalar perturbation must be negative in infrared regime, we can avoid tachyon instability by considering strong Hubble friction. Additionally, we estimate the backreaction from the perturbations on background geometry, especially, against anisotropic perturbation in closed FLRW spacetime. It turns out that certain types of bouncing solution may be spoiled even if all perturbation modes are stable. 
Yosuke Misonoh, Mitsuhiro Fukushima, Shoichiro Miyashita
gr-qc hep-th