Deformation quantization of cosmological models
Ruben Cordero, Hugo Garcia-Compean, Francisco J. Turrubiates
TL;DR
This paper applies deformation quantization to various cosmological models, deriving Wigner functions analytically and numerically, to explore quantum cosmology in different scenarios including de Sitter, Kantowski-Sachs, and string cosmology.
Contribution
It provides explicit deformation quantization procedures and Wigner function calculations for multiple cosmological models, advancing the understanding of quantum cosmology in this formalism.
Findings
Wigner functions computed for de Sitter, Kantowski-Sachs, and string cosmology models.
Numerical results for Hartle-Hawking, Vilenkin, and Linde wave functions.
Analytical solutions for baby universe models.
Abstract
The Weyl-Wigner-Groenewold-Moyal formalism of deformation quantization is applied to cosmological models in the minisuperspace. The quantization procedure is performed explicitly for quantum cosmology in a flat minisuperspace. The de Sitter cosmological model is worked out in detail and the computation of the Wigner functions for the Hartle-Hawking, Vilenkin and Linde wave functions are done numerically. The Wigner function is analytically calculated for the Kantowski-Sachs model in (non)commutative quantum cosmology and for string cosmology with dilaton exponential potential. Finally, baby universes solutions are described in this context and the Wigner function is obtained.
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