Dynamical Properties of the Mukhanov-Sasaki Hamiltonian

Kobler M, Giesel K (2018)

Publication Language: English

Publication Type: Thesis

Publication year: 2018


The inflationary epoch at the beginning of the universe is commonly described within the frame- work of (linear) cosmological perturbation theory. The corresponding equation of motion for the gauge-invariant perturbations is the Mukhanov-Sasaki equation, which resembles a time-dependent harmonic oscillator. At first we will consider a mechanical analogue of the Mukhanov-Sasaki equa- tion and use the known Lewis-Riesenfeld invariant and the extended phase space formalism in- troduced in previous works in order to analyse the system. These techniques allow to construct an extended canonical transformation that maps an explicitly time-dependent Hamiltonian into a time-independent one. The generators of this symplectic map can in turn be canonically quan- tised on the original part of the phase space, which is the constraint hypersurface of the extended theory, connecting to recent publications. 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 associ- ated Dyson series. We will analyse the characteristic properties of this time-evolution operator and discuss whether it can be extended to the full Fock space. Finally we give an outlook towards possible applications of these techniques to inflationary quantum cosmology.

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How to cite


Kobler, M., & Giesel, K. (2018). Dynamical Properties of the Mukhanov-Sasaki Hamiltonian (Master thesis).


Kobler, Michael, and Kristina Giesel. Dynamical Properties of the Mukhanov-Sasaki Hamiltonian. Master thesis, 2018.

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