## Abstract

We investigate the detailed structure of the solution space of the Bianchi type I spacetime with a massless scalar field in loop quantum cosmology (LQC). To analyze the dynamics we use the effective Hamiltonian written by new gauge-invariant variables which have a more direct physical interpretation. Since the effective equations of motion contain a nontrivial quantum correction, we may regard the universes as classical when the dynamics is well-described by the classical Friedmann equation. In addition to solutions which evolve into the classical universes, we find cyclic and stationary solutions which are dominated by the quantum effect for all time. We also show the asymmetric behavior and completely classify the Kasner transition across the bounce moment. We calculate the "probability" of having a classical isotropic universe by using the measure defined by the volume form in the solution space. Although we find that isotropic classical universes are disfavored in our model with a massless scalar field, we argue that LQC can explain the present isotropy if we consider a more realistic model.

Original language | English |
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Article number | 064013 |

Journal | Physical Review D - Particles, Fields, Gravitation and Cosmology |

Volume | 87 |

Issue number | 6 |

DOIs | |

Publication status | Published - 2013 Mar 12 |

## ASJC Scopus subject areas

- Nuclear and High Energy Physics
- Physics and Astronomy (miscellaneous)