TL;DR
This paper introduces quantum cosmology, focusing on its conceptual foundations, formalism, and key issues like the problem of time, boundary conditions, and singularity avoidance within quantum geometrodynamics.
Contribution
It provides a comprehensive overview of the formalism and conceptual challenges in quantum cosmology, emphasizing the minisuperspace Wheeler--DeWitt approach.
Findings
Discussion of the problem of time in quantum cosmology
Analysis of boundary conditions and semiclassical approximation
Insights into singularity avoidance mechanisms
Abstract
We give an introduction into quantum cosmology with emphasis on its conceptual parts. After a general motivation we review the formalism of canonical quantum gravity on which discussions of quantum cosmology are usually based. We then present the minisuperspace Wheeler--DeWitt equation and elaborate on the problem of time, the imposition of boundary conditions, the semiclassical approximation, the origin of irreversibility, and singularity avoidance. Restriction is made to the framework of quantum geometrodynamics.
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