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GR: Fachverband Gravitation und Relativitätstheorie

GR 8: Quantum Cosmology and Quantum Gravity I

GR 8.4: Vortrag

Mittwoch, 20. März 2019, 15:15–15:30, HS 4

Dynamical Properties of the Mukhanov-Sasaki Hamiltonian — •Michael Kobler, Kristina Giesel, and Max Joseph Fahn — Institut für Quantengravitation, Friedrich-Alexander-Universität Erlangen-Nürnberg, Staudtstr. 7, 91058 Erlangen, Deutschland

In the context of linearized cosmological perturbation theory, the Mukhanov-Sasaki equation plays a pivotal role. Each mode of this equation resembles a time-dependent harmonic oscillator. We consider the single-mode Mukhanov-Sasaki Hamiltonian as a toy model in mechanics and use the known Lewis-Riesenfeld invariant and the extended phase space formalism introduced in previous works in order to analyze this system. These techniques allow to classically construct an extended canonical transformation that maps an explicitly time-dependent Hamiltonian into a time-independent one, as well as to implement the corresponding unitary map in the quantum theory. Our further analysis leads us to a closed form of the time-evolution operator for the single-mode Mukhanov-Sasaki Hamiltonian, that is to the associated Dyson series. Finally, we discuss an extension of these techniques to the bosonic Fock space, together with some applications for a quasi-de Sitter background.