Abstract
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.
Highlights
Spacetime singularity at the beginning of the Universe is a problem of great importance in standard cosmology
Based on the HL theory, the higher spatial curvatures in action possibly behave as such exotic matter
It is natural to consider that the effective exotic matter which violates the null energy condition destabilizes spacetime
Summary
Spacetime singularity at the beginning of the Universe is a problem of great importance in standard cosmology. A lot of attempts to resolve the singularity at the beginning of the Universe have been proposed based on an extension of GR [3], e.g., the superstring theory [4], loop quantum gravity [5], causal dynamical triangulation [6], and gravity with a nonlocal operator [7]. We set the goal of this paper to show the stability conditions for singularity-free cosmological solutions against a linearorder perturbation in anisotropic modes and inhomogeneity ones. Recalling our motivation to investigate spacetime stabilities of singularity-free solutions, it is necessary to see the dynamics of tensor and vector degree of freedoms as well as scalar ones.
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