Würzburg 2018 – scientific programme

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GR: Fachverband Gravitation und Relativitätstheorie

GR 16: Quantum Gravity III

GR 16.6: Talk

Friday, March 23, 2018, 12:15–12:30, NW-Bau - HS3

Integrable Liouville Cosmological Models: The self-adjointness of Hamiltonian and the Semi-classical Wave Functions — Alexander Andrianov^1,4, Chen Lan², Oleg Novikov¹, and •Yi-Fan Wang³ — ¹Saint-Petersburg State University, Ulyanovskaya str. 1, Petrodvorets, Sankt-Petersburg 198504, Russland — ²ELI-ALPS Research Institute, Budapesti út 5, H-67228 Szeged, Ungarn — ³Institut für Theoretische Physik, Universität zu Köln, Zülpicher Straße 77, D-50937 Köln, Deutschland — ⁴Institut de Ciències del Cosmos, Universitat de Barcelona, Martí i Franquès 1, E-08028 Barcelona, Spanien

The Friedmann--Lemaître cosmological model with a Liouville field is investigated in the context of classical and quantum geometrodynamics. An integral of motion is used to eliminate the lapse function, and explicit classical solutions are obtained as implicit curves.

In the quantum theory of bounded above quintessence model and phantom model, the matter Hamiltonian allows a family of self-adjoint extensions, leading to the non-trivial removal of the degeneracy and discretisation of the levels, respectively.

The semi-classical wave functions are studied by the WKB approximation as well as numerically with the Schrödinger and Mostafazadeh inner products, and are compared with the classical trajectories.