# Quantum Cosmology with Dynamic Vacuum in a Minimum-Length Setting.

Name: Michael França Gusson

Type: PhD thesis

Publication date: 16/03/2021

Advisor:

Name | Role |
---|---|

José Alexandre Nogueira | Advisor * |

Examining board:

Name | Role |
---|---|

Bernardo Brunoro Dilem | External Examiner * |

Flavio Gimenes Alvarenga | External Examiner * |

Hermano Endlich Schneider Velten | Internal Examiner * |

José Alexandre Nogueira | Advisor * |

Júlio César Fabris | Internal Examiner * |

Nivaldo Agostinho Lemos | External Examiner * |

Raphael Góes Furtado | Co advisor * |

Summary: Theories that propose the unification of general relativity and quantum mechanics, for example the String Theory, point to the existence of a minimum value of observable length. The existence of this implies a generalization of the Heisenbergs uncertainty principle, so as to no more admit a null uncertainty in position, thus modifying the algebra of quantum mechanics. According to the cosmological model of the Big Bang, the Universe is expanding,which it means that it was very small in the past, so its nature was fundamentally quantum. Thus, it is necessary to build a quantum description of the evolution of the Universe, under the context of modified algebra due to the existence of a minimum length.

In this work, was considered the effects in a dynamic vacuum cosmological model, due to the presence of a minimum length introduced by a GUP (generalized uncertainty principle) related to the modified commutation relation [^x,^p] = iℏ/1-β^P² e The wave function of

the Universe, which is the solution of the Wheeler-DeWitti equation in the representation of the quasiposition space, was found at the limit for small values of the scale factor.