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**Modified cosmological equations and the Einstein static universe.**
*(English)*
Zbl 1246.83048

There is a renewed interest in the Einstein static (ES) Universe since it could play a crucial role as an initial state for a past-eternal inflationary cosmological model. However, the original closed model, given as an exact solution of Einstein’s equations with a cosmological constant, is unstable to homogeneous perturbations. Therefore, by employing dynamical system techniques and numerical integrations, the authors consider solutions and their stability in the framework of loop quantum cosmology and Horava-Lifshitz gravity. It is shown that in the first case, beside the ES solution of classical general relativity, a solution also arises for open cosmological models, whose stability behavior is completely characterized. In the second case, two solutions are found along with their stability properties.

Reviewer: Horst-Heino von Borzeszkowski (Berlin)

### MSC:

83C15 | Exact solutions to problems in general relativity and gravitational theory |

83F05 | Relativistic cosmology |

83C45 | Quantization of the gravitational field |

83D05 | Relativistic gravitational theories other than Einstein’s, including asymmetric field theories |

83-08 | Computational methods for problems pertaining to relativity and gravitational theory |

37N20 | Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics) |

83C75 | Space-time singularities, cosmic censorship, etc. |