Integrable Minisuperspace Models with Liouville Field: Energy Density Self-Adjointness and Semiclassical Wave Packets

Abstract

The homogeneous cosmological models with a Liouville scalar field are investigated in classical and quantum context of Wheeler-DeWitt geometrodynamics. In the quantum case of quintessence field with potential unbounded from below and phantom field, the energy density operators are not essentially self-adjoint and self-adjoint extensions contain ambiguities. Therefore the same classical actions correspond to a family of distinct quantum models. For the phantom field the energy spectrum happens to be discrete. The probability conservation and appropriate classical limit can be achieved with a certain restriction of the functional class. The appropriately localized wave packets are studied numerically using the Schrodinger's norm and a conserved Mostafazadeh's norm introduced from techniques of pseudo-Hermitian quantum mechanics. These norms give a similar packet evolution that is confronted with analytical classical solutions.

Main points emphasized, less important material shortened; 24 pages, 13 figures

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• Accelerating cosmologies in an integrable model with noncommutative minisuperspace variables
• Classical and quantum cosmology of $K$-essentially modified $R^2$ and pure $R^p$ gravity
• Semi-classical predictions of cosmological wave-packets from ridge-lines
• Pseudo-hermitian Chebyshev differential matrix and non-Hermitian Liouville quantum mechanics