München 2019 – scientific programme
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GR: Fachverband Gravitation und Relativitätstheorie
GR 11: Quantum Cosmology and Quantum Gravity II
GR 11.2: Talk
Thursday, March 21, 2019, 11:15–11:30, HS 5
Hamiltonian diagonalization in hybrid quantum cosmology — •Beatriz Elizaga Navascués1, Guillermo A. Mena Marugán2, and Thomas Thiemann1 — 1Institute for Quantum Gravity, Friedrich-Alexander University Erlangen-Nürnberg, Staudstraße 7, 91058 Erlangen, Germany — 2Instituto de Estructura de la Materia, IEM-CSIC, Serrano 121, 28006 Madrid, Spain
In this work, we explore the possibility of selecting a natural vacuum state for scalar and tensor gauge-invariant cosmological perturbations in the context of hybrid quantum cosmology. For that, we make use of a canonical formulation of the entire cosmological system (background geometry and perturbations) in which the gauge-invariant degrees of freedom are identified as canonical variables. Introducing background-dependent linear canonical transformations that respect the spatial symmetries of the background on the gauge-invariant perturbations, and completing these transformations in the entire system, we are able to characterize a generic collection of annihilation and creationlike variables that obey the dynamics dictated by a respective collection of Hamiltonians. We then impose that such Hamiltonians display no self-interaction terms, and thus in a Fock representation with normal ordering they act diagonally on the basis of n-particle states. This leads to a very precise characterization of the allowed annihilation and creationlike variables, which we argue can be further restricted to a unique choice under some physical considerations. Finally, we discuss the relation of our selected vacuum and the standard adiabatic vacua in the context of quantum field theory in curved spacetimes.